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"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = | VolumeMapping(cc, rconn, gel=gel) | sfepy.fem.mappings.VolumeMapping |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = | SurfaceMapping(dual_coors, tri_conn, gel=gel) | sfepy.fem.mappings.SurfaceMapping |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = | FESurface(None, self.region, self.gel.faces, conn, ig) | sfepy.fem.fe_surface.FESurface |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= | la.norm_l2_along_axis(centre_normals) | sfepy.linalg.norm_l2_along_axis |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = SurfaceMapping(dual_coors, tri_conn, gel=gel)
# Compute triangle basis (edge) vectors.
nn = surface.nodes[ueo]
edge_coors = mesh_coors[nn]
edge_centre_coors = 0.5 * edge_coors.sum(axis=1)
edge_normals = 0.5 * nodal_normals[ueo].sum(axis=1)
edge_normals /= | la.norm_l2_along_axis(edge_normals) | sfepy.linalg.norm_l2_along_axis |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = SurfaceMapping(dual_coors, tri_conn, gel=gel)
# Compute triangle basis (edge) vectors.
nn = surface.nodes[ueo]
edge_coors = mesh_coors[nn]
edge_centre_coors = 0.5 * edge_coors.sum(axis=1)
edge_normals = 0.5 * nodal_normals[ueo].sum(axis=1)
edge_normals /= la.norm_l2_along_axis(edge_normals)[:,None]
nn = surface.nodes[ueo]
edge_dirs = edge_coors[:,1] - edge_coors[:,0]
edge_dirs /= | la.norm_l2_along_axis(edge_dirs) | sfepy.linalg.norm_l2_along_axis |
"""
Friction-slip model formulated as the implicit complementarity problem.
To integrate over a (dual) mesh, one needs:
* coordinates of element vertices
* element connectivity
* local base for each element
* constant in each sub-triangle of the dual mesh
Data for each dual element:
* connectivity of its sub-triangles
* base directions t_1, t_2
Normal stresses:
* Assemble the rezidual and apply the LCBC operator described below.
Solution in \hat{V}_h^c:
* construct a restriction operator via LCBC just like in the no-penetration case
* use the substitution:
u_1 = n_1 * w
u_2 = n_2 * w
u_3 = n_3 * w
The new DOF is `w`.
* for the record, no-penetration does:
w_1 = - (1 / n_1) * (u_2 * n_2 + u_3 * n_3)
w_2 = u_2
w_3 = u_3
"""
from sfepy.base.base import *
from sfepy.base.compat import unique
import sfepy.linalg as la
from sfepy.fem import Mesh, Domain, Field, Variables
from sfepy.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.fem.fe_surface import FESurface
from sfepy.fem.utils import compute_nodal_normals
def edge_data_to_output(coors, conn, e_sort, data):
out = nm.zeros_like(coors)
out[conn[e_sort,0]] = data
return Struct(name='output_data',
mode='vertex', data=out,
dofs=None)
class DualMesh(Struct):
"""Dual mesh corresponding to a (surface) region."""
def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3,), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None,:])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = SurfaceMapping(dual_coors, tri_conn, gel=gel)
# Compute triangle basis (edge) vectors.
nn = surface.nodes[ueo]
edge_coors = mesh_coors[nn]
edge_centre_coors = 0.5 * edge_coors.sum(axis=1)
edge_normals = 0.5 * nodal_normals[ueo].sum(axis=1)
edge_normals /= la.norm_l2_along_axis(edge_normals)[:,None]
nn = surface.nodes[ueo]
edge_dirs = edge_coors[:,1] - edge_coors[:,0]
edge_dirs /= la.norm_l2_along_axis(edge_dirs)[:,None]
edge_ortho = nm.cross(edge_normals, edge_dirs)
edge_ortho /= | la.norm_l2_along_axis(edge_ortho) | sfepy.linalg.norm_l2_along_axis |
# -*- coding: utf-8 -*-
r"""
Linear elasticity with given displacements.
Find :math:`\ul{u}` such that:
.. math::
\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
= 0
\;, \quad \forall \ul{v} \;,
where
.. math::
D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) +
\lambda \ \delta_{ij} \delta_{kl}
\;.
This example models a cylinder that is fixed at one end while the second end
has a specified displacement of 0.01 in the x direction (this boundary
condition is named ``'Displaced'``). There is also a specified displacement of
0.005 in the z direction for points in the region labeled
``'SomewhereTop'``. This boundary condition is named
``'PerturbedSurface'``. The region ``'SomewhereTop'`` is specified as those
vertices for which::
(z > 0.017) & (x > 0.03) & (x < 0.07)
The displacement field (three DOFs/node) in the ``'Omega region'`` is
approximated using P1 (four-node tetrahedral) finite elements. The material is
linear elastic and its properties are specified as Lamé parameters
:math:`\lambda` and :math:`\mu` (see
http://en.wikipedia.org/wiki/Lam%C3%A9_parameters)
The output is the displacement for each vertex, saved by default to
cylinder.vtk. View the results using::
$ ./postproc.py cylinder.vtk --wireframe -b --only-names=u -d'u,plot_displacements,rel_scaling=1'
"""
from sfepy import data_dir
from sfepy.mechanics.matcoefs import stiffness_from_lame
filename_mesh = data_dir + '/meshes/3d/cylinder.mesh'
regions = {
'Omega' : 'all',
'Left' : ('vertices in (x < 0.001)', 'facet'),
'Right' : ('vertices in (x > 0.099)', 'facet'),
'SomewhereTop' : ('vertices in (z > 0.017) & (x > 0.03) & (x < 0.07)',
'vertex'),
}
materials = {
'solid' : ({'D': | stiffness_from_lame(dim=3, lam=1e1, mu=1e0) | sfepy.mechanics.matcoefs.stiffness_from_lame |
import os
import numpy as nm
try:
from enthought.tvtk.api import tvtk
from enthought.mayavi.sources.vtk_data_source import VTKDataSource
from enthought.pyface.timer.api import Timer
except:
from tvtk.api import tvtk
from mayavi.sources.vtk_data_source import VTKDataSource
from pyface.timer.api import Timer
from dataset_manager import DatasetManager
from sfepy.base.base import Struct, basestr
from sfepy.postprocess.utils import mlab
from sfepy.discrete.fem import Mesh
from sfepy.discrete.fem.meshio import MeshIO, vtk_cell_types, supported_formats
def create_file_source(filename, watch=False, offscreen=True):
"""Factory function to create a file source corresponding to the
given file format."""
kwargs = {'watch' : watch, 'offscreen' : offscreen}
if isinstance(filename, basestr):
fmt = os.path.splitext(filename)[1]
is_sequence = False
else: # A sequence.
fmt = os.path.splitext(filename[0])[1]
is_sequence = True
fmt = fmt.lower()
if fmt == '.vtk':
# VTK is supported directly by Mayavi, no need to use MeshIO.
if is_sequence:
return VTKSequenceFileSource(filename, **kwargs)
else:
return VTKFileSource(filename, **kwargs)
elif fmt in supported_formats.keys():
if is_sequence:
if fmt == '.h5':
raise ValueError('format .h5 does not support file sequences!')
else:
return GenericSequenceFileSource(filename, **kwargs)
else:
return GenericFileSource(filename, **kwargs)
else:
raise ValueError('unknown file format! (%s)' % fmt)
class FileSource(Struct):
"""General file source."""
def __init__(self, filename, watch=False, offscreen=True):
"""Create a file source using the given file name."""
mlab.options.offscreen = offscreen
self.watch = watch
self.filename = filename
self.reset()
def __call__(self, step=0):
"""Get the file source."""
if self.source is None:
self.source = self.create_source()
if self.watch:
self.timer = Timer(1000, self.poll_file)
return self.source
def reset(self):
"""Reset."""
self.mat_id_name = None
self.source = None
self.notify_obj = None
self.steps = []
self.times = []
self.step = 0
self.time = 0.0
if self.watch:
self.last_stat = os.stat(self.filename)
def setup_mat_id(self, mat_id_name='mat_id', single_color=False):
self.mat_id_name = mat_id_name
self.single_color = single_color
def get_step_time(self, step=None, time=None):
"""
Set current step and time to the values closest greater or equal to
either step or time. Return the found values.
"""
if (step is not None) and len(self.steps):
step = step if step >= 0 else self.steps[-1] + step + 1
ii = nm.searchsorted(self.steps, step)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
if len(self.times):
self.time = self.times[ii]
elif (time is not None) and len(self.times):
ii = nm.searchsorted(self.times, time)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
self.time = self.times[ii]
return self.step, self.time
def get_ts_info(self):
return self.steps, self.times
def get_mat_id(self, mat_id_name='mat_id'):
"""
Get material ID numbers of the underlying mesh elements.
"""
if self.source is not None:
dm = DatasetManager(dataset=self.source.outputs[0])
mat_id = dm.cell_scalars[mat_id_name]
return mat_id
def file_changed(self):
pass
def setup_notification(self, obj, attr):
"""The attribute 'attr' of the object 'obj' will be set to True
when the source file is watched and changes."""
self.notify_obj = obj
self.notify_attr = attr
def poll_file(self):
"""Check the source file's time stamp and notify the
self.notify_obj in case it changed. Subclasses should implement
the file_changed() method."""
if not self.notify_obj:
return
s = os.stat(self.filename)
if s[-2] == self.last_stat[-2]:
setattr(self.notify_obj, self.notify_attr, False)
else:
self.file_changed()
setattr(self.notify_obj, self.notify_attr, True)
self.last_stat = s
class VTKFileSource(FileSource):
"""A thin wrapper around mlab.pipeline.open()."""
def create_source(self):
"""Create a VTK file source """
return | mlab.pipeline.open(self.filename) | sfepy.postprocess.utils.mlab.pipeline.open |
import os
import numpy as nm
try:
from enthought.tvtk.api import tvtk
from enthought.mayavi.sources.vtk_data_source import VTKDataSource
from enthought.pyface.timer.api import Timer
except:
from tvtk.api import tvtk
from mayavi.sources.vtk_data_source import VTKDataSource
from pyface.timer.api import Timer
from dataset_manager import DatasetManager
from sfepy.base.base import Struct, basestr
from sfepy.postprocess.utils import mlab
from sfepy.discrete.fem import Mesh
from sfepy.discrete.fem.meshio import MeshIO, vtk_cell_types, supported_formats
def create_file_source(filename, watch=False, offscreen=True):
"""Factory function to create a file source corresponding to the
given file format."""
kwargs = {'watch' : watch, 'offscreen' : offscreen}
if isinstance(filename, basestr):
fmt = os.path.splitext(filename)[1]
is_sequence = False
else: # A sequence.
fmt = os.path.splitext(filename[0])[1]
is_sequence = True
fmt = fmt.lower()
if fmt == '.vtk':
# VTK is supported directly by Mayavi, no need to use MeshIO.
if is_sequence:
return VTKSequenceFileSource(filename, **kwargs)
else:
return VTKFileSource(filename, **kwargs)
elif fmt in supported_formats.keys():
if is_sequence:
if fmt == '.h5':
raise ValueError('format .h5 does not support file sequences!')
else:
return GenericSequenceFileSource(filename, **kwargs)
else:
return GenericFileSource(filename, **kwargs)
else:
raise ValueError('unknown file format! (%s)' % fmt)
class FileSource(Struct):
"""General file source."""
def __init__(self, filename, watch=False, offscreen=True):
"""Create a file source using the given file name."""
mlab.options.offscreen = offscreen
self.watch = watch
self.filename = filename
self.reset()
def __call__(self, step=0):
"""Get the file source."""
if self.source is None:
self.source = self.create_source()
if self.watch:
self.timer = Timer(1000, self.poll_file)
return self.source
def reset(self):
"""Reset."""
self.mat_id_name = None
self.source = None
self.notify_obj = None
self.steps = []
self.times = []
self.step = 0
self.time = 0.0
if self.watch:
self.last_stat = os.stat(self.filename)
def setup_mat_id(self, mat_id_name='mat_id', single_color=False):
self.mat_id_name = mat_id_name
self.single_color = single_color
def get_step_time(self, step=None, time=None):
"""
Set current step and time to the values closest greater or equal to
either step or time. Return the found values.
"""
if (step is not None) and len(self.steps):
step = step if step >= 0 else self.steps[-1] + step + 1
ii = nm.searchsorted(self.steps, step)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
if len(self.times):
self.time = self.times[ii]
elif (time is not None) and len(self.times):
ii = nm.searchsorted(self.times, time)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
self.time = self.times[ii]
return self.step, self.time
def get_ts_info(self):
return self.steps, self.times
def get_mat_id(self, mat_id_name='mat_id'):
"""
Get material ID numbers of the underlying mesh elements.
"""
if self.source is not None:
dm = DatasetManager(dataset=self.source.outputs[0])
mat_id = dm.cell_scalars[mat_id_name]
return mat_id
def file_changed(self):
pass
def setup_notification(self, obj, attr):
"""The attribute 'attr' of the object 'obj' will be set to True
when the source file is watched and changes."""
self.notify_obj = obj
self.notify_attr = attr
def poll_file(self):
"""Check the source file's time stamp and notify the
self.notify_obj in case it changed. Subclasses should implement
the file_changed() method."""
if not self.notify_obj:
return
s = os.stat(self.filename)
if s[-2] == self.last_stat[-2]:
setattr(self.notify_obj, self.notify_attr, False)
else:
self.file_changed()
setattr(self.notify_obj, self.notify_attr, True)
self.last_stat = s
class VTKFileSource(FileSource):
"""A thin wrapper around mlab.pipeline.open()."""
def create_source(self):
"""Create a VTK file source """
return mlab.pipeline.open(self.filename)
def get_bounding_box(self):
bbox = nm.array(self.source.reader.unstructured_grid_output.bounds)
return bbox.reshape((3,2)).T
def set_filename(self, filename, vis_source):
self.filename = filename
vis_source.base_file_name = filename
# Force re-read.
vis_source.reader.modified()
vis_source.update()
# Propagate changes in the pipeline.
vis_source.data_changed = True
class VTKSequenceFileSource(VTKFileSource):
"""A thin wrapper around mlab.pipeline.open() for VTK file sequences."""
def __init__(self, *args, **kwargs):
FileSource.__init__(self, *args, **kwargs)
self.steps = nm.arange(len(self.filename), dtype=nm.int32)
def create_source(self):
"""Create a VTK file source """
return | mlab.pipeline.open(self.filename[0]) | sfepy.postprocess.utils.mlab.pipeline.open |
import os
import numpy as nm
try:
from enthought.tvtk.api import tvtk
from enthought.mayavi.sources.vtk_data_source import VTKDataSource
from enthought.pyface.timer.api import Timer
except:
from tvtk.api import tvtk
from mayavi.sources.vtk_data_source import VTKDataSource
from pyface.timer.api import Timer
from dataset_manager import DatasetManager
from sfepy.base.base import Struct, basestr
from sfepy.postprocess.utils import mlab
from sfepy.discrete.fem import Mesh
from sfepy.discrete.fem.meshio import MeshIO, vtk_cell_types, supported_formats
def create_file_source(filename, watch=False, offscreen=True):
"""Factory function to create a file source corresponding to the
given file format."""
kwargs = {'watch' : watch, 'offscreen' : offscreen}
if isinstance(filename, basestr):
fmt = os.path.splitext(filename)[1]
is_sequence = False
else: # A sequence.
fmt = os.path.splitext(filename[0])[1]
is_sequence = True
fmt = fmt.lower()
if fmt == '.vtk':
# VTK is supported directly by Mayavi, no need to use MeshIO.
if is_sequence:
return VTKSequenceFileSource(filename, **kwargs)
else:
return VTKFileSource(filename, **kwargs)
elif fmt in supported_formats.keys():
if is_sequence:
if fmt == '.h5':
raise ValueError('format .h5 does not support file sequences!')
else:
return GenericSequenceFileSource(filename, **kwargs)
else:
return GenericFileSource(filename, **kwargs)
else:
raise ValueError('unknown file format! (%s)' % fmt)
class FileSource(Struct):
"""General file source."""
def __init__(self, filename, watch=False, offscreen=True):
"""Create a file source using the given file name."""
mlab.options.offscreen = offscreen
self.watch = watch
self.filename = filename
self.reset()
def __call__(self, step=0):
"""Get the file source."""
if self.source is None:
self.source = self.create_source()
if self.watch:
self.timer = Timer(1000, self.poll_file)
return self.source
def reset(self):
"""Reset."""
self.mat_id_name = None
self.source = None
self.notify_obj = None
self.steps = []
self.times = []
self.step = 0
self.time = 0.0
if self.watch:
self.last_stat = os.stat(self.filename)
def setup_mat_id(self, mat_id_name='mat_id', single_color=False):
self.mat_id_name = mat_id_name
self.single_color = single_color
def get_step_time(self, step=None, time=None):
"""
Set current step and time to the values closest greater or equal to
either step or time. Return the found values.
"""
if (step is not None) and len(self.steps):
step = step if step >= 0 else self.steps[-1] + step + 1
ii = nm.searchsorted(self.steps, step)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
if len(self.times):
self.time = self.times[ii]
elif (time is not None) and len(self.times):
ii = nm.searchsorted(self.times, time)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
self.time = self.times[ii]
return self.step, self.time
def get_ts_info(self):
return self.steps, self.times
def get_mat_id(self, mat_id_name='mat_id'):
"""
Get material ID numbers of the underlying mesh elements.
"""
if self.source is not None:
dm = DatasetManager(dataset=self.source.outputs[0])
mat_id = dm.cell_scalars[mat_id_name]
return mat_id
def file_changed(self):
pass
def setup_notification(self, obj, attr):
"""The attribute 'attr' of the object 'obj' will be set to True
when the source file is watched and changes."""
self.notify_obj = obj
self.notify_attr = attr
def poll_file(self):
"""Check the source file's time stamp and notify the
self.notify_obj in case it changed. Subclasses should implement
the file_changed() method."""
if not self.notify_obj:
return
s = os.stat(self.filename)
if s[-2] == self.last_stat[-2]:
setattr(self.notify_obj, self.notify_attr, False)
else:
self.file_changed()
setattr(self.notify_obj, self.notify_attr, True)
self.last_stat = s
class VTKFileSource(FileSource):
"""A thin wrapper around mlab.pipeline.open()."""
def create_source(self):
"""Create a VTK file source """
return mlab.pipeline.open(self.filename)
def get_bounding_box(self):
bbox = nm.array(self.source.reader.unstructured_grid_output.bounds)
return bbox.reshape((3,2)).T
def set_filename(self, filename, vis_source):
self.filename = filename
vis_source.base_file_name = filename
# Force re-read.
vis_source.reader.modified()
vis_source.update()
# Propagate changes in the pipeline.
vis_source.data_changed = True
class VTKSequenceFileSource(VTKFileSource):
"""A thin wrapper around mlab.pipeline.open() for VTK file sequences."""
def __init__(self, *args, **kwargs):
FileSource.__init__(self, *args, **kwargs)
self.steps = nm.arange(len(self.filename), dtype=nm.int32)
def create_source(self):
"""Create a VTK file source """
return mlab.pipeline.open(self.filename[0])
def set_filename(self, filename, vis_source):
self.filename = filename
vis_source.base_file_name = filename[self.step]
class GenericFileSource(FileSource):
"""File source usable with any format supported by MeshIO classes."""
def __init__(self, *args, **kwargs):
FileSource.__init__(self, *args, **kwargs)
self.read_common(self.filename)
def read_common(self, filename):
self.io = | MeshIO.any_from_filename(filename) | sfepy.discrete.fem.meshio.MeshIO.any_from_filename |
import os
import numpy as nm
try:
from enthought.tvtk.api import tvtk
from enthought.mayavi.sources.vtk_data_source import VTKDataSource
from enthought.pyface.timer.api import Timer
except:
from tvtk.api import tvtk
from mayavi.sources.vtk_data_source import VTKDataSource
from pyface.timer.api import Timer
from dataset_manager import DatasetManager
from sfepy.base.base import Struct, basestr
from sfepy.postprocess.utils import mlab
from sfepy.discrete.fem import Mesh
from sfepy.discrete.fem.meshio import MeshIO, vtk_cell_types, supported_formats
def create_file_source(filename, watch=False, offscreen=True):
"""Factory function to create a file source corresponding to the
given file format."""
kwargs = {'watch' : watch, 'offscreen' : offscreen}
if isinstance(filename, basestr):
fmt = os.path.splitext(filename)[1]
is_sequence = False
else: # A sequence.
fmt = os.path.splitext(filename[0])[1]
is_sequence = True
fmt = fmt.lower()
if fmt == '.vtk':
# VTK is supported directly by Mayavi, no need to use MeshIO.
if is_sequence:
return VTKSequenceFileSource(filename, **kwargs)
else:
return VTKFileSource(filename, **kwargs)
elif fmt in supported_formats.keys():
if is_sequence:
if fmt == '.h5':
raise ValueError('format .h5 does not support file sequences!')
else:
return GenericSequenceFileSource(filename, **kwargs)
else:
return GenericFileSource(filename, **kwargs)
else:
raise ValueError('unknown file format! (%s)' % fmt)
class FileSource(Struct):
"""General file source."""
def __init__(self, filename, watch=False, offscreen=True):
"""Create a file source using the given file name."""
mlab.options.offscreen = offscreen
self.watch = watch
self.filename = filename
self.reset()
def __call__(self, step=0):
"""Get the file source."""
if self.source is None:
self.source = self.create_source()
if self.watch:
self.timer = Timer(1000, self.poll_file)
return self.source
def reset(self):
"""Reset."""
self.mat_id_name = None
self.source = None
self.notify_obj = None
self.steps = []
self.times = []
self.step = 0
self.time = 0.0
if self.watch:
self.last_stat = os.stat(self.filename)
def setup_mat_id(self, mat_id_name='mat_id', single_color=False):
self.mat_id_name = mat_id_name
self.single_color = single_color
def get_step_time(self, step=None, time=None):
"""
Set current step and time to the values closest greater or equal to
either step or time. Return the found values.
"""
if (step is not None) and len(self.steps):
step = step if step >= 0 else self.steps[-1] + step + 1
ii = nm.searchsorted(self.steps, step)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
if len(self.times):
self.time = self.times[ii]
elif (time is not None) and len(self.times):
ii = nm.searchsorted(self.times, time)
ii = nm.clip(ii, 0, len(self.steps) - 1)
self.step = self.steps[ii]
self.time = self.times[ii]
return self.step, self.time
def get_ts_info(self):
return self.steps, self.times
def get_mat_id(self, mat_id_name='mat_id'):
"""
Get material ID numbers of the underlying mesh elements.
"""
if self.source is not None:
dm = DatasetManager(dataset=self.source.outputs[0])
mat_id = dm.cell_scalars[mat_id_name]
return mat_id
def file_changed(self):
pass
def setup_notification(self, obj, attr):
"""The attribute 'attr' of the object 'obj' will be set to True
when the source file is watched and changes."""
self.notify_obj = obj
self.notify_attr = attr
def poll_file(self):
"""Check the source file's time stamp and notify the
self.notify_obj in case it changed. Subclasses should implement
the file_changed() method."""
if not self.notify_obj:
return
s = os.stat(self.filename)
if s[-2] == self.last_stat[-2]:
setattr(self.notify_obj, self.notify_attr, False)
else:
self.file_changed()
setattr(self.notify_obj, self.notify_attr, True)
self.last_stat = s
class VTKFileSource(FileSource):
"""A thin wrapper around mlab.pipeline.open()."""
def create_source(self):
"""Create a VTK file source """
return mlab.pipeline.open(self.filename)
def get_bounding_box(self):
bbox = nm.array(self.source.reader.unstructured_grid_output.bounds)
return bbox.reshape((3,2)).T
def set_filename(self, filename, vis_source):
self.filename = filename
vis_source.base_file_name = filename
# Force re-read.
vis_source.reader.modified()
vis_source.update()
# Propagate changes in the pipeline.
vis_source.data_changed = True
class VTKSequenceFileSource(VTKFileSource):
"""A thin wrapper around mlab.pipeline.open() for VTK file sequences."""
def __init__(self, *args, **kwargs):
FileSource.__init__(self, *args, **kwargs)
self.steps = nm.arange(len(self.filename), dtype=nm.int32)
def create_source(self):
"""Create a VTK file source """
return mlab.pipeline.open(self.filename[0])
def set_filename(self, filename, vis_source):
self.filename = filename
vis_source.base_file_name = filename[self.step]
class GenericFileSource(FileSource):
"""File source usable with any format supported by MeshIO classes."""
def __init__(self, *args, **kwargs):
FileSource.__init__(self, *args, **kwargs)
self.read_common(self.filename)
def read_common(self, filename):
self.io = MeshIO.any_from_filename(filename)
self.steps, self.times, _ = self.io.read_times()
self.mesh = | Mesh.from_file(filename) | sfepy.discrete.fem.Mesh.from_file |
import os
import numpy as nm
try:
from enthought.tvtk.api import tvtk
from enthought.mayavi.sources.vtk_data_source import VTKDataSource
from enthought.pyface.timer.api import Timer
except:
from tvtk.api import tvtk
from mayavi.sources.vtk_data_source import VTKDataSource
from pyface.timer.api import Timer
from dataset_manager import DatasetManager
from sfepy.base.base import Struct, basestr
from sfepy.postprocess.utils import mlab
from sfepy.discrete.fem import Mesh
from sfepy.discrete.fem.meshio import MeshIO, vtk_cell_types, supported_formats
def create_file_source(filename, watch=False, offscreen=True):
"""Factory function to create a file source corresponding to the
given file format."""
kwargs = {'watch' : watch, 'offscreen' : offscreen}
if isinstance(filename, basestr):
fmt = os.path.splitext(filename)[1]
is_sequence = False
else: # A sequence.
fmt = os.path.splitext(filename[0])[1]
is_sequence = True
fmt = fmt.lower()
if fmt == '.vtk':
# VTK is supported directly by Mayavi, no need to use MeshIO.
if is_sequence:
return VTKSequenceFileSource(filename, **kwargs)
else:
return VTKFileSource(filename, **kwargs)
elif fmt in | supported_formats.keys() | sfepy.discrete.fem.meshio.supported_formats.keys |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in | iter_dict_of_lists(conn_info, return_keys=True) | sfepy.base.base.iter_dict_of_lists |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += get_paths('sfepy/discrete/structural/fields*.py')
Field._all = load_classes(field_files, [Field], ignore_errors=True,
name_attr='family_name')
table = Field._all
space = conf.get('space', 'H1')
poly_space_base = conf.get('poly_space_base', 'lagrange')
key = space + '_' + poly_space_base
approx_order = parse_approx_order(conf.approx_order)
ao, force_bubble, discontinuous = approx_order
region = regions[conf.region]
if region.kind == 'cell':
# Volume fields.
kind = 'volume'
if discontinuous:
cls = table[kind + '_' + key + '_discontinuous']
else:
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
else:
# Surface fields.
kind = 'surface'
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
return obj
def _setup_kind(self):
name = self.get('family_name', None,
'An abstract Field method called!')
aux = name.split('_')
self.space = aux[1]
self.poly_space_base = aux[2]
def clear_mappings(self, clear_all=False):
"""
Clear current reference mappings.
"""
self.mappings = {}
if clear_all:
if hasattr(self, 'mappings0'):
self.mappings0.clear()
else:
self.mappings0 = {}
def save_mappings(self):
"""
Save current reference mappings to `mappings0` attribute.
"""
import sfepy.base.multiproc as multi
if | multi.is_remote_dict(self.mappings0) | sfepy.base.multiproc.is_remote_dict |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += get_paths('sfepy/discrete/structural/fields*.py')
Field._all = load_classes(field_files, [Field], ignore_errors=True,
name_attr='family_name')
table = Field._all
space = conf.get('space', 'H1')
poly_space_base = conf.get('poly_space_base', 'lagrange')
key = space + '_' + poly_space_base
approx_order = parse_approx_order(conf.approx_order)
ao, force_bubble, discontinuous = approx_order
region = regions[conf.region]
if region.kind == 'cell':
# Volume fields.
kind = 'volume'
if discontinuous:
cls = table[kind + '_' + key + '_discontinuous']
else:
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
else:
# Surface fields.
kind = 'surface'
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
return obj
def _setup_kind(self):
name = self.get('family_name', None,
'An abstract Field method called!')
aux = name.split('_')
self.space = aux[1]
self.poly_space_base = aux[2]
def clear_mappings(self, clear_all=False):
"""
Clear current reference mappings.
"""
self.mappings = {}
if clear_all:
if hasattr(self, 'mappings0'):
self.mappings0.clear()
else:
self.mappings0 = {}
def save_mappings(self):
"""
Save current reference mappings to `mappings0` attribute.
"""
import sfepy.base.multiproc as multi
if multi.is_remote_dict(self.mappings0):
for k, v in six.iteritems(self.mappings):
m, _ = self.mappings[k]
nv = (m.bf, m.bfg, m.det, m.volume, m.normal)
self.mappings0[k] = nv
else:
self.mappings0 = self.mappings.copy()
def get_mapping(self, region, integral, integration,
get_saved=False, return_key=False):
"""
For given region, integral and integration type, get a reference
mapping, i.e. jacobians, element volumes and base function
derivatives for Volume-type geometries, and jacobians, normals
and base function derivatives for Surface-type geometries
corresponding to the field approximation.
The mappings are cached in the field instance in `mappings`
attribute. The mappings can be saved to `mappings0` using
`Field.save_mappings`. The saved mapping can be retrieved by
passing `get_saved=True`. If the required (saved) mapping
is not in cache, a new one is created.
Returns
-------
geo : CMapping instance
The reference mapping.
mapping : VolumeMapping or SurfaceMapping instance
The mapping.
key : tuple
The key of the mapping in `mappings` or `mappings0`.
"""
import sfepy.base.multiproc as multi
key = (region.name, integral.order, integration)
if get_saved:
out = self.mappings0.get(key, None)
if multi.is_remote_dict(self.mappings0) and out is not None:
m, i = self.create_mapping(region, integral, integration)
m.bf[:], m.bfg[:], m.det[:], m.volume[:] = out[0:4]
if m.normal is not None:
m.normal[:] = m[4]
out = m, i
else:
out = self.mappings.get(key, None)
if out is None:
out = self.create_mapping(region, integral, integration)
self.mappings[key] = out
if return_key:
out = out + (key,)
return out
def create_eval_mesh(self):
"""
Create a mesh for evaluating the field. The default implementation
returns None, because this mesh is for most fields the same as the one
created by `Field.create_mesh()`.
"""
def evaluate_at(self, coors, source_vals, mode='val', strategy='general',
close_limit=0.1, get_cells_fun=None, cache=None,
ret_cells=False, ret_status=False, ret_ref_coors=False,
verbose=False):
"""
Evaluate source DOF values corresponding to the field in the given
coordinates using the field interpolation.
Parameters
----------
coors : array, shape ``(n_coor, dim)``
The coordinates the source values should be interpolated into.
source_vals : array, shape ``(n_nod, n_components)``
The source DOF values corresponding to the field.
mode : {'val', 'grad'}, optional
The evaluation mode: the field value (default) or the field value
gradient.
strategy : {'general', 'convex'}, optional
The strategy for finding the elements that contain the
coordinates. For convex meshes, the 'convex' strategy might be
faster than the 'general' one.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
get_cells_fun : callable, optional
If given, a function with signature ``get_cells_fun(coors, cmesh,
**kwargs)`` returning cells and offsets that potentially contain
points with the coordinates `coors`. Applicable only when
`strategy` is 'general'. When not given,
:func:`get_potential_cells()
<sfepy.discrete.common.global_interp.get_potential_cells>` is used.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other
data can be cached. Optionally, the cache can also contain the
reference element coordinates as `cache.ref_coors`, `cache.cells`
and `cache.status`, if the evaluation occurs in the same
coordinates repeatedly. In that case the mesh related data are
ignored. See :func:`Field.get_evaluate_cache()
<sfepy.discrete.fem.fields_base.FEField.get_evaluate_cache()>`.
ret_ref_coors : bool, optional
If True, return also the found reference element coordinates.
ret_status : bool, optional
If True, return also the enclosing cell status for each point.
ret_cells : bool, optional
If True, return also the cell indices the coordinates are in.
verbose : bool
If False, reduce verbosity.
Returns
-------
vals : array
The interpolated values with shape ``(n_coor, n_components)`` or
gradients with shape ``(n_coor, n_components, dim)`` according to
the `mode`. If `ret_status` is False, the values where the status
is greater than one are set to ``numpy.nan``.
ref_coors : array
The found reference element coordinates, if `ret_ref_coors` is True.
cells : array
The cell indices, if `ret_ref_coors` or `ret_cells` or `ret_status`
are True.
status : array
The status, if `ret_ref_coors` or `ret_status` are True, with the
following meaning: 0 is success, 1 is extrapolation within
`close_limit`, 2 is extrapolation outside `close_limit`, 3 is
failure, 4 is failure due to non-convergence of the Newton
iteration in tensor product cells. If close_limit is 0, then for
the 'general' strategy the status 5 indicates points outside of the
field domain that had no potential cells.
"""
from sfepy.discrete.common.global_interp import get_ref_coors
from sfepy.discrete.common.extmods.crefcoors import evaluate_in_rc
from sfepy.base.base import complex_types
| output('evaluating in %d points...' % coors.shape[0], verbose=verbose) | sfepy.base.base.output |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += get_paths('sfepy/discrete/structural/fields*.py')
Field._all = load_classes(field_files, [Field], ignore_errors=True,
name_attr='family_name')
table = Field._all
space = conf.get('space', 'H1')
poly_space_base = conf.get('poly_space_base', 'lagrange')
key = space + '_' + poly_space_base
approx_order = parse_approx_order(conf.approx_order)
ao, force_bubble, discontinuous = approx_order
region = regions[conf.region]
if region.kind == 'cell':
# Volume fields.
kind = 'volume'
if discontinuous:
cls = table[kind + '_' + key + '_discontinuous']
else:
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
else:
# Surface fields.
kind = 'surface'
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
return obj
def _setup_kind(self):
name = self.get('family_name', None,
'An abstract Field method called!')
aux = name.split('_')
self.space = aux[1]
self.poly_space_base = aux[2]
def clear_mappings(self, clear_all=False):
"""
Clear current reference mappings.
"""
self.mappings = {}
if clear_all:
if hasattr(self, 'mappings0'):
self.mappings0.clear()
else:
self.mappings0 = {}
def save_mappings(self):
"""
Save current reference mappings to `mappings0` attribute.
"""
import sfepy.base.multiproc as multi
if multi.is_remote_dict(self.mappings0):
for k, v in six.iteritems(self.mappings):
m, _ = self.mappings[k]
nv = (m.bf, m.bfg, m.det, m.volume, m.normal)
self.mappings0[k] = nv
else:
self.mappings0 = self.mappings.copy()
def get_mapping(self, region, integral, integration,
get_saved=False, return_key=False):
"""
For given region, integral and integration type, get a reference
mapping, i.e. jacobians, element volumes and base function
derivatives for Volume-type geometries, and jacobians, normals
and base function derivatives for Surface-type geometries
corresponding to the field approximation.
The mappings are cached in the field instance in `mappings`
attribute. The mappings can be saved to `mappings0` using
`Field.save_mappings`. The saved mapping can be retrieved by
passing `get_saved=True`. If the required (saved) mapping
is not in cache, a new one is created.
Returns
-------
geo : CMapping instance
The reference mapping.
mapping : VolumeMapping or SurfaceMapping instance
The mapping.
key : tuple
The key of the mapping in `mappings` or `mappings0`.
"""
import sfepy.base.multiproc as multi
key = (region.name, integral.order, integration)
if get_saved:
out = self.mappings0.get(key, None)
if multi.is_remote_dict(self.mappings0) and out is not None:
m, i = self.create_mapping(region, integral, integration)
m.bf[:], m.bfg[:], m.det[:], m.volume[:] = out[0:4]
if m.normal is not None:
m.normal[:] = m[4]
out = m, i
else:
out = self.mappings.get(key, None)
if out is None:
out = self.create_mapping(region, integral, integration)
self.mappings[key] = out
if return_key:
out = out + (key,)
return out
def create_eval_mesh(self):
"""
Create a mesh for evaluating the field. The default implementation
returns None, because this mesh is for most fields the same as the one
created by `Field.create_mesh()`.
"""
def evaluate_at(self, coors, source_vals, mode='val', strategy='general',
close_limit=0.1, get_cells_fun=None, cache=None,
ret_cells=False, ret_status=False, ret_ref_coors=False,
verbose=False):
"""
Evaluate source DOF values corresponding to the field in the given
coordinates using the field interpolation.
Parameters
----------
coors : array, shape ``(n_coor, dim)``
The coordinates the source values should be interpolated into.
source_vals : array, shape ``(n_nod, n_components)``
The source DOF values corresponding to the field.
mode : {'val', 'grad'}, optional
The evaluation mode: the field value (default) or the field value
gradient.
strategy : {'general', 'convex'}, optional
The strategy for finding the elements that contain the
coordinates. For convex meshes, the 'convex' strategy might be
faster than the 'general' one.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
get_cells_fun : callable, optional
If given, a function with signature ``get_cells_fun(coors, cmesh,
**kwargs)`` returning cells and offsets that potentially contain
points with the coordinates `coors`. Applicable only when
`strategy` is 'general'. When not given,
:func:`get_potential_cells()
<sfepy.discrete.common.global_interp.get_potential_cells>` is used.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other
data can be cached. Optionally, the cache can also contain the
reference element coordinates as `cache.ref_coors`, `cache.cells`
and `cache.status`, if the evaluation occurs in the same
coordinates repeatedly. In that case the mesh related data are
ignored. See :func:`Field.get_evaluate_cache()
<sfepy.discrete.fem.fields_base.FEField.get_evaluate_cache()>`.
ret_ref_coors : bool, optional
If True, return also the found reference element coordinates.
ret_status : bool, optional
If True, return also the enclosing cell status for each point.
ret_cells : bool, optional
If True, return also the cell indices the coordinates are in.
verbose : bool
If False, reduce verbosity.
Returns
-------
vals : array
The interpolated values with shape ``(n_coor, n_components)`` or
gradients with shape ``(n_coor, n_components, dim)`` according to
the `mode`. If `ret_status` is False, the values where the status
is greater than one are set to ``numpy.nan``.
ref_coors : array
The found reference element coordinates, if `ret_ref_coors` is True.
cells : array
The cell indices, if `ret_ref_coors` or `ret_cells` or `ret_status`
are True.
status : array
The status, if `ret_ref_coors` or `ret_status` are True, with the
following meaning: 0 is success, 1 is extrapolation within
`close_limit`, 2 is extrapolation outside `close_limit`, 3 is
failure, 4 is failure due to non-convergence of the Newton
iteration in tensor product cells. If close_limit is 0, then for
the 'general' strategy the status 5 indicates points outside of the
field domain that had no potential cells.
"""
from sfepy.discrete.common.global_interp import get_ref_coors
from sfepy.discrete.common.extmods.crefcoors import evaluate_in_rc
from sfepy.base.base import complex_types
output('evaluating in %d points...' % coors.shape[0], verbose=verbose)
ref_coors, cells, status = get_ref_coors(self, coors,
strategy=strategy,
close_limit=close_limit,
get_cells_fun=get_cells_fun,
cache=cache,
verbose=verbose)
timer = | Timer(start=True) | sfepy.base.timing.Timer |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += get_paths('sfepy/discrete/structural/fields*.py')
Field._all = load_classes(field_files, [Field], ignore_errors=True,
name_attr='family_name')
table = Field._all
space = conf.get('space', 'H1')
poly_space_base = conf.get('poly_space_base', 'lagrange')
key = space + '_' + poly_space_base
approx_order = parse_approx_order(conf.approx_order)
ao, force_bubble, discontinuous = approx_order
region = regions[conf.region]
if region.kind == 'cell':
# Volume fields.
kind = 'volume'
if discontinuous:
cls = table[kind + '_' + key + '_discontinuous']
else:
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
else:
# Surface fields.
kind = 'surface'
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
return obj
def _setup_kind(self):
name = self.get('family_name', None,
'An abstract Field method called!')
aux = name.split('_')
self.space = aux[1]
self.poly_space_base = aux[2]
def clear_mappings(self, clear_all=False):
"""
Clear current reference mappings.
"""
self.mappings = {}
if clear_all:
if hasattr(self, 'mappings0'):
self.mappings0.clear()
else:
self.mappings0 = {}
def save_mappings(self):
"""
Save current reference mappings to `mappings0` attribute.
"""
import sfepy.base.multiproc as multi
if multi.is_remote_dict(self.mappings0):
for k, v in six.iteritems(self.mappings):
m, _ = self.mappings[k]
nv = (m.bf, m.bfg, m.det, m.volume, m.normal)
self.mappings0[k] = nv
else:
self.mappings0 = self.mappings.copy()
def get_mapping(self, region, integral, integration,
get_saved=False, return_key=False):
"""
For given region, integral and integration type, get a reference
mapping, i.e. jacobians, element volumes and base function
derivatives for Volume-type geometries, and jacobians, normals
and base function derivatives for Surface-type geometries
corresponding to the field approximation.
The mappings are cached in the field instance in `mappings`
attribute. The mappings can be saved to `mappings0` using
`Field.save_mappings`. The saved mapping can be retrieved by
passing `get_saved=True`. If the required (saved) mapping
is not in cache, a new one is created.
Returns
-------
geo : CMapping instance
The reference mapping.
mapping : VolumeMapping or SurfaceMapping instance
The mapping.
key : tuple
The key of the mapping in `mappings` or `mappings0`.
"""
import sfepy.base.multiproc as multi
key = (region.name, integral.order, integration)
if get_saved:
out = self.mappings0.get(key, None)
if multi.is_remote_dict(self.mappings0) and out is not None:
m, i = self.create_mapping(region, integral, integration)
m.bf[:], m.bfg[:], m.det[:], m.volume[:] = out[0:4]
if m.normal is not None:
m.normal[:] = m[4]
out = m, i
else:
out = self.mappings.get(key, None)
if out is None:
out = self.create_mapping(region, integral, integration)
self.mappings[key] = out
if return_key:
out = out + (key,)
return out
def create_eval_mesh(self):
"""
Create a mesh for evaluating the field. The default implementation
returns None, because this mesh is for most fields the same as the one
created by `Field.create_mesh()`.
"""
def evaluate_at(self, coors, source_vals, mode='val', strategy='general',
close_limit=0.1, get_cells_fun=None, cache=None,
ret_cells=False, ret_status=False, ret_ref_coors=False,
verbose=False):
"""
Evaluate source DOF values corresponding to the field in the given
coordinates using the field interpolation.
Parameters
----------
coors : array, shape ``(n_coor, dim)``
The coordinates the source values should be interpolated into.
source_vals : array, shape ``(n_nod, n_components)``
The source DOF values corresponding to the field.
mode : {'val', 'grad'}, optional
The evaluation mode: the field value (default) or the field value
gradient.
strategy : {'general', 'convex'}, optional
The strategy for finding the elements that contain the
coordinates. For convex meshes, the 'convex' strategy might be
faster than the 'general' one.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
get_cells_fun : callable, optional
If given, a function with signature ``get_cells_fun(coors, cmesh,
**kwargs)`` returning cells and offsets that potentially contain
points with the coordinates `coors`. Applicable only when
`strategy` is 'general'. When not given,
:func:`get_potential_cells()
<sfepy.discrete.common.global_interp.get_potential_cells>` is used.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other
data can be cached. Optionally, the cache can also contain the
reference element coordinates as `cache.ref_coors`, `cache.cells`
and `cache.status`, if the evaluation occurs in the same
coordinates repeatedly. In that case the mesh related data are
ignored. See :func:`Field.get_evaluate_cache()
<sfepy.discrete.fem.fields_base.FEField.get_evaluate_cache()>`.
ret_ref_coors : bool, optional
If True, return also the found reference element coordinates.
ret_status : bool, optional
If True, return also the enclosing cell status for each point.
ret_cells : bool, optional
If True, return also the cell indices the coordinates are in.
verbose : bool
If False, reduce verbosity.
Returns
-------
vals : array
The interpolated values with shape ``(n_coor, n_components)`` or
gradients with shape ``(n_coor, n_components, dim)`` according to
the `mode`. If `ret_status` is False, the values where the status
is greater than one are set to ``numpy.nan``.
ref_coors : array
The found reference element coordinates, if `ret_ref_coors` is True.
cells : array
The cell indices, if `ret_ref_coors` or `ret_cells` or `ret_status`
are True.
status : array
The status, if `ret_ref_coors` or `ret_status` are True, with the
following meaning: 0 is success, 1 is extrapolation within
`close_limit`, 2 is extrapolation outside `close_limit`, 3 is
failure, 4 is failure due to non-convergence of the Newton
iteration in tensor product cells. If close_limit is 0, then for
the 'general' strategy the status 5 indicates points outside of the
field domain that had no potential cells.
"""
from sfepy.discrete.common.global_interp import get_ref_coors
from sfepy.discrete.common.extmods.crefcoors import evaluate_in_rc
from sfepy.base.base import complex_types
output('evaluating in %d points...' % coors.shape[0], verbose=verbose)
ref_coors, cells, status = get_ref_coors(self, coors,
strategy=strategy,
close_limit=close_limit,
get_cells_fun=get_cells_fun,
cache=cache,
verbose=verbose)
timer = Timer(start=True)
# Interpolate to the reference coordinates.
source_dtype = nm.float64 if source_vals.dtype in complex_types\
else source_vals.dtype
if mode == 'val':
vals = nm.empty((coors.shape[0], source_vals.shape[1], 1),
dtype=source_dtype)
cmode = 0
elif mode == 'grad':
vals = nm.empty((coors.shape[0], source_vals.shape[1],
coors.shape[1]),
dtype=source_dtype)
cmode = 1
ctx = self.create_basis_context()
if source_vals.dtype in complex_types:
valsi = vals.copy()
evaluate_in_rc(vals, ref_coors, cells, status,
nm.ascontiguousarray(source_vals.real),
self.get_econn('volume', self.region), cmode, ctx)
evaluate_in_rc(valsi, ref_coors, cells, status,
nm.ascontiguousarray(source_vals.imag),
self.get_econn('volume', self.region), cmode, ctx)
vals = vals + valsi * 1j
else:
evaluate_in_rc(vals, ref_coors, cells, status, source_vals,
self.get_econn('volume', self.region), cmode, ctx)
output('interpolation: %f s' % timer.stop(),verbose=verbose)
| output('...done',verbose=verbose) | sfepy.base.base.output |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += | get_paths('sfepy/discrete/iga/fields*.py') | sfepy.get_paths |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += | get_paths('sfepy/discrete/structural/fields*.py') | sfepy.get_paths |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in get_paths('sfepy/discrete/fem/fields*.py')
if 'fields_base.py' not in ii]
field_files += get_paths('sfepy/discrete/iga/fields*.py')
field_files += get_paths('sfepy/discrete/structural/fields*.py')
Field._all = load_classes(field_files, [Field], ignore_errors=True,
name_attr='family_name')
table = Field._all
space = conf.get('space', 'H1')
poly_space_base = conf.get('poly_space_base', 'lagrange')
key = space + '_' + poly_space_base
approx_order = parse_approx_order(conf.approx_order)
ao, force_bubble, discontinuous = approx_order
region = regions[conf.region]
if region.kind == 'cell':
# Volume fields.
kind = 'volume'
if discontinuous:
cls = table[kind + '_' + key + '_discontinuous']
else:
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
else:
# Surface fields.
kind = 'surface'
cls = table[kind + '_' + key]
obj = cls(conf.name, conf.dtype, conf.shape, region,
approx_order=approx_order[:2])
return obj
def _setup_kind(self):
name = self.get('family_name', None,
'An abstract Field method called!')
aux = name.split('_')
self.space = aux[1]
self.poly_space_base = aux[2]
def clear_mappings(self, clear_all=False):
"""
Clear current reference mappings.
"""
self.mappings = {}
if clear_all:
if hasattr(self, 'mappings0'):
self.mappings0.clear()
else:
self.mappings0 = {}
def save_mappings(self):
"""
Save current reference mappings to `mappings0` attribute.
"""
import sfepy.base.multiproc as multi
if multi.is_remote_dict(self.mappings0):
for k, v in six.iteritems(self.mappings):
m, _ = self.mappings[k]
nv = (m.bf, m.bfg, m.det, m.volume, m.normal)
self.mappings0[k] = nv
else:
self.mappings0 = self.mappings.copy()
def get_mapping(self, region, integral, integration,
get_saved=False, return_key=False):
"""
For given region, integral and integration type, get a reference
mapping, i.e. jacobians, element volumes and base function
derivatives for Volume-type geometries, and jacobians, normals
and base function derivatives for Surface-type geometries
corresponding to the field approximation.
The mappings are cached in the field instance in `mappings`
attribute. The mappings can be saved to `mappings0` using
`Field.save_mappings`. The saved mapping can be retrieved by
passing `get_saved=True`. If the required (saved) mapping
is not in cache, a new one is created.
Returns
-------
geo : CMapping instance
The reference mapping.
mapping : VolumeMapping or SurfaceMapping instance
The mapping.
key : tuple
The key of the mapping in `mappings` or `mappings0`.
"""
import sfepy.base.multiproc as multi
key = (region.name, integral.order, integration)
if get_saved:
out = self.mappings0.get(key, None)
if | multi.is_remote_dict(self.mappings0) | sfepy.base.multiproc.is_remote_dict |
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, iter_dict_of_lists, Struct, basestr
from sfepy.base.timing import Timer
import six
def parse_approx_order(approx_order):
"""
Parse the uniform approximation order value (str or int).
"""
ao_msg = 'unsupported approximation order! (%s)'
force_bubble = False
discontinuous = False
if approx_order is None:
return 'iga', force_bubble, discontinuous
elif isinstance(approx_order, basestr):
if approx_order.startswith('iga'):
return approx_order, force_bubble, discontinuous
try:
ao = int(approx_order)
except ValueError:
mode = approx_order[-1].lower()
if mode == 'b':
ao = int(approx_order[:-1])
force_bubble = True
elif mode == 'd':
ao = int(approx_order[:-1])
discontinuous = True
else:
raise ValueError(ao_msg % approx_order)
if ao < 0:
raise ValueError(ao_msg % approx_order)
elif ao == 0:
discontinuous = True
return ao, force_bubble, discontinuous
def parse_shape(shape, dim):
if isinstance(shape, basestr):
try:
shape = {'scalar' : (1,),
'vector' : (dim,)}[shape]
except KeyError:
raise ValueError('unsupported field shape! (%s)', shape)
elif isinstance(shape, six.integer_types):
shape = (int(shape),)
return shape
def setup_extra_data(conn_info):
"""
Setup extra data required for non-volume integration.
"""
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
for var in info.all_vars:
field = var.get_field()
if var == info.primary:
field.setup_extra_data(info.ps_tg, info, info.is_trace)
def fields_from_conf(conf, regions):
fields = {}
for key, val in six.iteritems(conf):
field = Field.from_conf(val, regions)
fields[field.name] = field
return fields
class Field(Struct):
"""
Base class for fields.
"""
_all = None
@staticmethod
def from_args(name, dtype, shape, region, approx_order=1,
space='H1', poly_space_base='lagrange'):
"""
Create a Field subclass instance corresponding to a given space.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int/str
The FE approximation order, e.g. 0, 1, 2, '1B' (1 with bubble).
space : str
The function space name.
poly_space_base : str
The name of polynomial space base.
Notes
-----
Assumes one cell type for the whole region!
"""
conf = Struct(name=name, dtype=dtype, shape=shape, region=region.name,
approx_order=approx_order, space=space,
poly_space_base=poly_space_base)
return Field.from_conf(conf, {region.name : region})
@staticmethod
def from_conf(conf, regions):
"""
Create a Field subclass instance based on the configuration.
"""
if Field._all is None:
from sfepy import get_paths
from sfepy.base.base import load_classes
field_files = [ii for ii
in | get_paths('sfepy/discrete/fem/fields*.py') | sfepy.get_paths |
import numpy as nm
from sfepy.base.base import output, Struct
from sfepy.base.conf import ProblemConf, get_standard_keywords
from sfepy.homogenization.homogen_app import HomogenizationApp
from sfepy.homogenization.coefficients import Coefficients
import tables as pt
from sfepy.discrete.fem.meshio import HDF5MeshIO
import os.path as op
def get_homog_coefs_linear(ts, coor, mode,
micro_filename=None, regenerate=False,
coefs_filename=None):
oprefix = output.prefix
output.prefix = 'micro:'
required, other = | get_standard_keywords() | sfepy.base.conf.get_standard_keywords |
import numpy as nm
from sfepy.base.base import output, Struct
from sfepy.base.conf import ProblemConf, get_standard_keywords
from sfepy.homogenization.homogen_app import HomogenizationApp
from sfepy.homogenization.coefficients import Coefficients
import tables as pt
from sfepy.discrete.fem.meshio import HDF5MeshIO
import os.path as op
def get_homog_coefs_linear(ts, coor, mode,
micro_filename=None, regenerate=False,
coefs_filename=None):
oprefix = output.prefix
output.prefix = 'micro:'
required, other = get_standard_keywords()
required.remove( 'equations' )
conf = | ProblemConf.from_file(micro_filename, required, other, verbose=False) | sfepy.base.conf.ProblemConf.from_file |
import numpy as nm
from sfepy.base.base import output, Struct
from sfepy.base.conf import ProblemConf, get_standard_keywords
from sfepy.homogenization.homogen_app import HomogenizationApp
from sfepy.homogenization.coefficients import Coefficients
import tables as pt
from sfepy.discrete.fem.meshio import HDF5MeshIO
import os.path as op
def get_homog_coefs_linear(ts, coor, mode,
micro_filename=None, regenerate=False,
coefs_filename=None):
oprefix = output.prefix
output.prefix = 'micro:'
required, other = get_standard_keywords()
required.remove( 'equations' )
conf = ProblemConf.from_file(micro_filename, required, other, verbose=False)
if coefs_filename is None:
coefs_filename = conf.options.get('coefs_filename', 'coefs')
coefs_filename = op.join(conf.options.get('output_dir', '.'),
coefs_filename) + '.h5'
if not regenerate:
if op.exists( coefs_filename ):
if not pt.isHDF5File( coefs_filename ):
regenerate = True
else:
regenerate = True
if regenerate:
options = Struct( output_filename_trunk = None )
app = HomogenizationApp( conf, options, 'micro:' )
coefs = app()
if type(coefs) is tuple:
coefs = coefs[0]
coefs.to_file_hdf5( coefs_filename )
else:
coefs = Coefficients.from_file_hdf5( coefs_filename )
out = {}
if mode == None:
for key, val in coefs.__dict__.iteritems():
out[key] = val
elif mode == 'qp':
for key, val in coefs.__dict__.iteritems():
if type( val ) == nm.ndarray or type(val) == nm.float64:
out[key] = nm.tile( val, (coor.shape[0], 1, 1) )
elif type(val) == dict:
for key2, val2 in val.iteritems():
if type(val2) == nm.ndarray or type(val2) == nm.float64:
out[key+'_'+key2] = \
nm.tile(val2, (coor.shape[0], 1, 1))
else:
out = None
output.prefix = oprefix
return out
def get_correctors_from_file( coefs_filename = 'coefs.h5',
dump_names = None ):
if dump_names == None:
coefs = Coefficients.from_file_hdf5( coefs_filename )
if hasattr( coefs, 'dump_names' ):
dump_names = coefs.dump_names
else:
raise ValueError( ' "filenames" coefficient must be used!' )
out = {}
for key, val in dump_names.iteritems():
corr_name = op.split( val )[-1]
io = | HDF5MeshIO( val+'.h5' ) | sfepy.discrete.fem.meshio.HDF5MeshIO |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = | Mesh.from_region(omega_gi, mesh, localize=True) | sfepy.discrete.fem.Mesh.from_region |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = | FEDomain('domain_i', mesh_i) | sfepy.discrete.fem.FEDomain |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
| output('number of local field DOFs:', field_i.n_nod) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = | FieldVariable('u_i', 'unknown', field_i) | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = | FieldVariable('v_i', 'test', field_i, primary_var_name='u_i') | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = | Integral('i', order=2*order) | sfepy.discrete.Integral |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = | Material('m', lam=10, mu=5) | sfepy.discrete.Material |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = | Equation('balance', t1 - 100 * t2) | sfepy.discrete.Equation |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = | Equations([eq]) | sfepy.discrete.Equations |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = | Problem('problem_i', equations=eqs, active_only=False) | sfepy.discrete.Problem |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = | pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose) | sfepy.parallel.parallel.verify_task_dof_maps |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
| output('rank', rank, 'of', size) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = | Struct() | sfepy.base.base.Struct |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = | Timer('solve_timer') | sfepy.base.timing.Timer |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = | Mesh.from_file(mesh_filename) | sfepy.discrete.fem.Mesh.from_file |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
| output('creating global domain and field...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = | FEDomain('domain', mesh) | sfepy.discrete.fem.FEDomain |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = | Field.from_args('fu', nm.float64, 1, omega, approx_order=order) | sfepy.discrete.fem.Field.from_args |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
| output('distributing field %s...' % field.name) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
| output('creating local problem...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = | Region.from_cells(lfd.cells, field.domain) | sfepy.discrete.common.region.Region.from_cells |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
| output('allocating global system...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = | pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1) | sfepy.parallel.parallel.get_sizes |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
| output('sizes:', sizes) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
| output('drange:', drange) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = | pl.get_local_ordering(field_i, lfd.petsc_dofs_conn) | sfepy.parallel.parallel.get_local_ordering |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
| output('pdofs:', pdofs) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
| output('evaluating local problem...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = | State(variables) | sfepy.discrete.State |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
| output('assembling global system...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
| apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc) | sfepy.discrete.evaluate.apply_ebc_to_matrix |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
| output('creating solver...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = | PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status) | sfepy.solvers.ls.PETScKrylovSolver |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
| output('solving...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = | pl.create_local_petsc_vector(pdofs) | sfepy.parallel.parallel.create_local_petsc_vector |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = | pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm) | sfepy.parallel.parallel.create_gather_scatter |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
| output('saving solution...') | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = | pl.create_gather_to_zero(psol) | sfepy.parallel.parallel.create_gather_to_zero |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
| output('...done in', timer.dt) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
| output.set_output(filename=filename, combined=options.silent == False) | sfepy.base.base.output.set_output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
| output('petsc options:', petsc_opts) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
| output('dimensions:', dims) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
| output('shape: ', shape) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
| output('centre: ', centre) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
output('centre: ', centre)
if comm.rank == 0:
from sfepy.mesh.mesh_generators import gen_block_mesh
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.mesh', '*.txt', '*.png'],
ignores=['output_log_%02d.txt' % ii
for ii in range(comm.size)],
verbose=True)
save_options(os.path.join(output_dir, 'options.txt'),
[('options', vars(options))])
mesh = gen_block_mesh(dims, shape, centre, name='block-fem',
verbose=True)
mesh.write(mesh_filename, io='auto')
comm.barrier()
| output('field order:', options.order) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
output('centre: ', centre)
if comm.rank == 0:
from sfepy.mesh.mesh_generators import gen_block_mesh
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.mesh', '*.txt', '*.png'],
ignores=['output_log_%02d.txt' % ii
for ii in range(comm.size)],
verbose=True)
save_options(os.path.join(output_dir, 'options.txt'),
[('options', vars(options))])
mesh = gen_block_mesh(dims, shape, centre, name='block-fem',
verbose=True)
mesh.write(mesh_filename, io='auto')
comm.barrier()
output('field order:', options.order)
stats = solve_problem(mesh_filename, options, comm)
| output(stats) | sfepy.base.base.output |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
| ensure_path(filename) | sfepy.base.ioutils.ensure_path |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
output('centre: ', centre)
if comm.rank == 0:
from sfepy.mesh.mesh_generators import gen_block_mesh
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.mesh', '*.txt', '*.png'],
ignores=['output_log_%02d.txt' % ii
for ii in range(comm.size)],
verbose=True)
save_options(os.path.join(output_dir, 'options.txt'),
[('options', vars(options))])
mesh = gen_block_mesh(dims, shape, centre, name='block-fem',
verbose=True)
mesh.write(mesh_filename, io='auto')
comm.barrier()
output('field order:', options.order)
stats = solve_problem(mesh_filename, options, comm)
output(stats)
if options.stats_filename:
if comm.rank == 0:
ensure_path(options.stats_filename)
comm.barrier()
pars = | Struct(dim=dim, shape=shape, order=options.order) | sfepy.base.base.Struct |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function= | Function('get_load', get_load) | sfepy.discrete.Function |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs= | Conditions([ebc1, ebc2]) | sfepy.discrete.conditions.Conditions |
#!/usr/bin/env python
r"""
Parallel assembling and solving of a Poisson's equation, using commands for
interactive use.
Find :math:`u` such that:
.. math::
\int_{\Omega} \nabla v \cdot \nabla u
= \int_{\Omega} v f
\;, \quad \forall s \;.
Important Notes
---------------
- This example requires petsc4py, mpi4py and (optionally) pymetis with their
dependencies installed!
- This example generates a number of files - do not use an existing non-empty
directory for the ``output_dir`` argument.
- Use the ``--clear`` option with care!
Notes
-----
- Each task is responsible for a subdomain consisting of a set of cells (a cell
region).
- Each subdomain owns PETSc DOFs within a consecutive range.
- When both global and task-local variables exist, the task-local
variables have ``_i`` suffix.
- This example does not use a nonlinear solver.
- This example can serve as a template for solving a linear single-field scalar
problem - just replace the equations in :func:`create_local_problem()`.
- The command line options are saved into <output_dir>/options.txt file.
Usage Examples
--------------
See all options::
$ python examples/diffusion/poisson_parallel_interactive.py -h
See PETSc options::
$ python examples/diffusion/poisson_parallel_interactive.py -help
Single process run useful for debugging with :func:`debug()
<sfepy.base.base.debug>`::
$ python examples/diffusion/poisson_parallel_interactive.py output-parallel
Parallel runs::
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101
$ mpiexec -n 3 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --metis
$ mpiexec -n 5 python examples/diffusion/poisson_parallel_interactive.py output-parallel -2 --shape=101,101 --verify --metis -ksp_monitor -ksp_converged_reason
View the results using::
$ python postproc.py output-parallel/sol.h5 --wireframe -b -d'u,plot_warp_scalar'
"""
from __future__ import absolute_import
from argparse import RawDescriptionHelpFormatter, ArgumentParser
import os
import sys
sys.path.append('.')
import csv
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import output, Struct
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.timing import Timer
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.discrete.common.region import Region
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem, State)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.evaluate import apply_ebc_to_matrix
from sfepy.terms import Term
from sfepy.solvers.ls import PETScKrylovSolver
import sfepy.parallel.parallel as pl
import sfepy.parallel.plot_parallel_dofs as ppd
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i,
approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2*order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral, omega_i, load=load, v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
verbose=False):
vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)
order = options.order
mesh = field.domain.mesh
sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
approx_order=order)
aux = FieldVariable('aux', 'parameter', sfield,
primary_var_name='(set-to-None)')
out = aux.create_output(vec,
linearization=Struct(kind='adaptive',
min_level=order-1,
max_level=order-1,
eps=1e-8))
filename = os.path.join(options.output_dir,
'para-domains-dofs.h5')
if field.is_higher_order():
out['aux'].mesh.write(filename, out=out)
else:
mesh.write(filename, out=out)
out = Struct(name='cells', mode='cell',
data=cell_tasks[:, None, None, None])
filename = os.path.join(options.output_dir,
'para-domains-cells.h5')
mesh.write(filename, out={'cells' : out})
def solve_problem(mesh_filename, options, comm):
order = options.order
rank, size = comm.Get_rank(), comm.Get_size()
output('rank', rank, 'of', size)
stats = Struct()
timer = Timer('solve_timer')
timer.start()
mesh = Mesh.from_file(mesh_filename)
stats.t_read_mesh = timer.stop()
timer.start()
if rank == 0:
cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
verbose=True)
else:
cell_tasks = None
stats.t_partition_mesh = timer.stop()
output('creating global domain and field...')
timer.start()
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
stats.t_create_global_fields = timer.stop()
output('...done in', timer.dt)
output('distributing field %s...' % field.name)
timer.start()
distribute = pl.distribute_fields_dofs
lfds, gfds = distribute([field], cell_tasks,
is_overlap=True,
save_inter_regions=options.save_inter_regions,
output_dir=options.output_dir,
comm=comm, verbose=True)
lfd = lfds[0]
stats.t_distribute_fields_dofs = timer.stop()
output('...done in', timer.dt)
if rank == 0:
dof_maps = gfds[0].dof_maps
id_map = gfds[0].id_map
if options.verify:
verify_save_dof_maps(field, cell_tasks,
dof_maps, id_map, options, verbose=True)
if options.plot:
ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
options.output_dir, size)
output('creating local problem...')
timer.start()
omega_gi = Region.from_cells(lfd.cells, field.domain)
omega_gi.finalize()
omega_gi.update_shape()
pb = create_local_problem(omega_gi, order)
variables = pb.get_variables()
eqs = pb.equations
u_i = variables['u_i']
field_i = u_i.field
stats.t_create_local_problem = timer.stop()
output('...done in', timer.dt)
if options.plot:
ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
options.output_dir, rank)
output('allocating global system...')
timer.start()
sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
output('sizes:', sizes)
output('drange:', drange)
pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)
output('pdofs:', pdofs)
pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
is_overlap=True, comm=comm,
verbose=True)
stats.t_allocate_global_system = timer.stop()
output('...done in', timer.dt)
output('evaluating local problem...')
timer.start()
state = State(variables)
state.fill(0.0)
state.apply_ebc()
rhs_i = eqs.eval_residuals(state())
# This must be after pl.create_petsc_system() call!
mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)
stats.t_evaluate_local_problem = timer.stop()
output('...done in', timer.dt)
output('assembling global system...')
timer.start()
apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
comm=comm, verbose=True)
stats.t_assemble_global_system = timer.stop()
output('...done in', timer.dt)
output('creating solver...')
timer.start()
conf = Struct(method='cg', precond='gamg', sub_precond='none',
i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
status = {}
ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)
stats.t_create_solver = timer.stop()
output('...done in', timer.dt)
output('solving...')
timer.start()
psol = ls(prhs, psol)
psol_i = pl.create_local_petsc_vector(pdofs)
gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)
scatter(psol_i, psol)
sol0_i = state() - psol_i[...]
psol_i[...] = sol0_i
gather(psol, psol_i)
stats.t_solve = timer.stop()
output('...done in', timer.dt)
output('saving solution...')
timer.start()
u_i.set_data(sol0_i)
out = u_i.create_output()
filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
pb.domain.mesh.write(filename, io='auto', out=out)
gather_to_zero = pl.create_gather_to_zero(psol)
psol_full = gather_to_zero(psol)
if comm.rank == 0:
sol = psol_full[...].copy()[id_map]
u = FieldVariable('u', 'parameter', field,
primary_var_name='(set-to-None)')
filename = os.path.join(options.output_dir, 'sol.h5')
if (order == 1) or (options.linearization == 'strip'):
out = u.create_output(sol)
mesh.write(filename, io='auto', out=out)
else:
out = u.create_output(sol, linearization=Struct(kind='adaptive',
min_level=0,
max_level=order,
eps=1e-3))
out['u'].mesh.write(filename, io='auto', out=out)
stats.t_save_solution = timer.stop()
output('...done in', timer.dt)
stats.t_total = timer.total
stats.n_dof = sizes[1]
stats.n_dof_local = sizes[0]
stats.n_cell = omega.shape.n_cell
stats.n_cell_local = omega_gi.shape.n_cell
if options.show:
plt.show()
return stats
def save_stats(filename, pars, stats, overwrite, rank, comm=None):
out = stats.to_dict()
names = sorted(out.keys())
shape_dict = {'n%d' % ii : pars.shape[ii] for ii in range(pars.dim)}
keys = ['size', 'rank', 'dim'] + list(shape_dict.keys()) + ['order'] + names
out['size'] = comm.size
out['rank'] = rank
out['dim'] = pars.dim
out.update(shape_dict)
out['order'] = pars.order
if rank == 0 and overwrite:
with open(filename, 'w') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writeheader()
writer.writerow(out)
else:
with open(filename, 'a') as fd:
writer = csv.DictWriter(fd, fieldnames=keys)
writer.writerow(out)
helps = {
'output_dir' :
'output directory',
'dims' :
'dimensions of the block [default: %(default)s]',
'shape' :
'shape (counts of nodes in x, y, z) of the block [default: %(default)s]',
'centre' :
'centre of the block [default: %(default)s]',
'2d' :
'generate a 2D rectangle, the third components of the above'
' options are ignored',
'order' :
'field approximation order',
'linearization' :
'linearization used for storing the results with approximation order > 1'
' [default: %(default)s]',
'metis' :
'use metis for domain partitioning',
'verify' :
'verify domain partitioning, save cells and DOFs of tasks'
' for visualization',
'plot' :
'make partitioning plots',
'save_inter_regions' :
'save inter-task regions for debugging partitioning problems',
'show' :
'show partitioning plots (implies --plot)',
'stats_filename' :
'name of the stats file for storing elapsed time statistics',
'new_stats' :
'create a new stats file with a header line (overwrites existing!)',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory'
' (DANGEROUS - use with care!)',
}
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='11,11,11', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--linearization', choices=['strip', 'adaptive'],
action='store', dest='linearization',
default='strip', help=helps['linearization'])
parser.add_argument('--metis',
action='store_true', dest='metis',
default=False, help=helps['metis'])
parser.add_argument('--verify',
action='store_true', dest='verify',
default=False, help=helps['verify'])
parser.add_argument('--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--show',
action='store_true', dest='show',
default=False, help=helps['show'])
parser.add_argument('--save-inter-regions',
action='store_true', dest='save_inter_regions',
default=False, help=helps['save_inter_regions'])
parser.add_argument('--stats', metavar='filename',
action='store', dest='stats_filename',
default=None, help=helps['stats_filename'])
parser.add_argument('--new-stats',
action='store_true', dest='new_stats',
default=False, help=helps['new_stats'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
options, petsc_opts = parser.parse_known_args()
if options.show:
options.plot = True
comm = pl.PETSc.COMM_WORLD
output_dir = options.output_dir
filename = os.path.join(output_dir, 'output_log_%02d.txt' % comm.rank)
if comm.rank == 0:
ensure_path(filename)
comm.barrier()
output.prefix = 'sfepy_%02d:' % comm.rank
output.set_output(filename=filename, combined=options.silent == False)
output('petsc options:', petsc_opts)
mesh_filename = os.path.join(options.output_dir, 'para.h5')
dim = 2 if options.is_2d else 3
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
output('centre: ', centre)
if comm.rank == 0:
from sfepy.mesh.mesh_generators import gen_block_mesh
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.mesh', '*.txt', '*.png'],
ignores=['output_log_%02d.txt' % ii
for ii in range(comm.size)],
verbose=True)
save_options(os.path.join(output_dir, 'options.txt'),
[('options', vars(options))])
mesh = gen_block_mesh(dims, shape, centre, name='block-fem',
verbose=True)
mesh.write(mesh_filename, io='auto')
comm.barrier()
output('field order:', options.order)
stats = solve_problem(mesh_filename, options, comm)
output(stats)
if options.stats_filename:
if comm.rank == 0:
| ensure_path(options.stats_filename) | sfepy.base.ioutils.ensure_path |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = | FEDomain('domain', mesh) | sfepy.discrete.fem.FEDomain |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = | define_box_regions(3, lbn, rtf) | sfepy.homogenization.utils.define_box_regions |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = | FieldVariable('u', 'unknown', vector_field, history=1) | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = | FieldVariable('v', 'test', vector_field, primary_var_name='u') | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = | FieldVariable('p', 'unknown', scalar_field, history=1) | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = | FieldVariable('q', 'test', scalar_field, primary_var_name='p') | sfepy.discrete.FieldVariable |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = | Function('disp_fun', get_displacement) | sfepy.discrete.Function |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = | Conditions([x_sym, y_sym, z_sym, displacement]) | sfepy.discrete.conditions.Conditions |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = | Integral('i', order=2*order+1) | sfepy.discrete.Integral |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = | Equation('balance', term_1 + term_pressure) | sfepy.discrete.Equation |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = | Equation('volume', term_volume_change - term_volume) | sfepy.discrete.Equation |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = | Equations([eq_balance, eq_volume]) | sfepy.discrete.Equations |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = Equations([eq_balance, eq_volume])
### Solvers ###
ls = | ScipyDirect({}) | sfepy.solvers.ls.ScipyDirect |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = Equations([eq_balance, eq_volume])
### Solvers ###
ls = ScipyDirect({})
nls_status = | IndexedStruct() | sfepy.base.base.IndexedStruct |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = Equations([eq_balance, eq_volume])
### Solvers ###
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton(
{'i_max' : 20},
lin_solver=ls, status=nls_status
)
### Problem ###
pb = | Problem('hyper', equations=equations) | sfepy.discrete.Problem |
#!/usr/bin/env python
r"""
This example shows the use of the `dw_tl_he_genyeoh` hyperelastic term, whose
contribution to the deformation energy density per unit reference volume is
given by
.. math::
W = K \, \left( \overline I_1 - 3 \right)^{p}
where :math:`\overline I_1` is the first main invariant of the deviatoric part
of the right Cauchy-Green deformation tensor :math:`\ull{C}` and `K` and `p`
are its parameters.
This term may be used to implement the generalized Yeoh hyperelastic material
model [1] by adding three such terms:
.. math::
W =
K_1 \, \left( \overline I_1 - 3 \right)^{m}
+K_2 \, \left( \overline I_1 - 3 \right)^{p}
+K_3 \, \left( \overline I_1 - 3 \right)^{q}
where the coefficients :math:`K_1, K_2, K_3` and exponents :math:`m, p, q` are
material parameters. Only a single term is used in this example for the sake of
simplicity.
Components of the second Piola-Kirchhoff stress are in the case of an
incompressible material
.. math::
S_{ij} = 2 \, \pdiff{W}{C_{ij}} - p \, F^{-1}_{ik} \, F^{-T}_{kj} \;,
where :math:`p` is the hydrostatic pressure.
The large deformation is described using the total Lagrangian formulation in
this example. The incompressibility is treated by mixed displacement-pressure
formulation. The weak formulation is:
Find the displacement field :math:`\ul{u}` and pressure field :math:`p`
such that:
.. math::
\intl{\Omega\suz}{} \ull{S}\eff(\ul{u}, p) : \ull{E}(\ul{v})
\difd{V} = 0
\;, \quad \forall \ul{v} \;,
\intl{\Omega\suz}{} q\, (J(\ul{u})-1) \difd{V} = 0
\;, \quad \forall q \;.
The following formula holds for the axial true (Cauchy) stress in the case of
uniaxial stress:
.. math::
\sigma(\lambda) =
\frac{2}{3} \, m \, K_1 \,
\left( \lambda^2 + \frac{2}{\lambda} - 3 \right)^{m-1} \,
\left( \lambda - \frac{1}{\lambda^2} \right) \;,
where :math:`\lambda = l/l_0` is the prescribed stretch (:math:`l_0` and
:math:`l` being the original and deformed specimen length respectively).
The boundary conditions are set so that a state of uniaxial stress is achieved,
i.e. appropriate components of displacement are fixed on the "Left", "Bottom",
and "Near" faces and a monotonously increasing displacement is prescribed on
the "Right" face. This prescribed displacement is then used to calculate
:math:`\lambda` and to convert the second Piola-Kirchhoff stress to the true
(Cauchy) stress.
Note on material parameters
---------------------------
The three-term generalized Yeoh model is meant to be used for modelling of
filled rubbers. The following choice of parameters is suggested [1] based on
experimental data and stability considerations:
:math:`K_1 > 0`,
:math:`K_2 < 0`,
:math:`K_3 > 0`,
:math:`0.7 < m < 1`,
:math:`m < p < q`.
Usage Examples
--------------
Default options::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py
To show a comparison of stress against the analytic formula::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -p
Using different mesh fineness::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--shape "5, 5, 5"
Different dimensions of the computational domain::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--dims "2, 1, 3"
Different length of time interval and/or number of time steps::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
-t 0,15,21
Use higher approximation order (the ``-t`` option to decrease the time step is
required for convergence here)::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py \
--order 2 -t 0,2,21
Change material parameters::
$ python examples/large_deformation/gen_yeoh_tl_up_interactive.py -m 2,1
View the results using ``resview.py``
-------------------------------------
Show pressure on deformed mesh (use PgDn/PgUp to jump forward/back)::
$ python resview.py --fields=p:f1:wu:p1 domain.??.vtk
Show the axial component of stress (second Piola-Kirchhoff)::
$ python resview.py --fields=stress:c0 domain.??.vtk
[1] <NAME>, <NAME>, <NAME>, <NAME>.
Busfield. Aconstitutive Model For Both Lowand High Strain Nonlinearities In
Highly Filled Elastomers And Implementation With User-Defined Material
Subroutines In Abaqus. Rubber Chemistry And Technology, Vol. 92, No. 4, Pp.
653-686 (2019)
"""
from __future__ import print_function, absolute_import
import argparse
import sys
SFEPY_DIR = '.'
sys.path.append(SFEPY_DIR)
import matplotlib.pyplot as plt
import numpy as np
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (
FieldVariable, Material, Integral, Function, Equation, Equations, Problem)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.discrete.fem import FEDomain, Field
from sfepy.homogenization.utils import define_box_regions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.solvers.ts_solvers import SimpleTimeSteppingSolver
from sfepy.terms import Term
DIMENSION = 3
def get_displacement(ts, coors, bc=None, problem=None):
"""
Define the time-dependent displacement.
"""
out = 1. * ts.time * coors[:, 0]
return out
def _get_analytic_stress(stretches, coef, exp):
out = np.array([
2 * coef * exp * (stretch**2 + 2 / stretch - 3)**(exp - 1)
* (stretch - stretch**-2)
if (stretch**2 + 2 / stretch > 3) else 0.
for stretch in stretches])
return out
def plot_graphs(
material_parameters, global_stress, global_displacement,
undeformed_length):
"""
Plot a comparison of the nominal stress computed by the FEM and using the
analytic formula.
Parameters
----------
material_parameters : list or tuple of float
The K_1 coefficient and exponent m.
global_displacement
The total displacement for each time step, from the FEM.
global_stress
The true (Cauchy) stress for each time step, from the FEM.
undeformed_length : float
The length of the undeformed specimen.
"""
coef, exp = material_parameters
stretch = 1 + np.array(global_displacement) / undeformed_length
# axial stress values
stress_fem_2pk = np.array([sig for sig in global_stress])
stress_fem = stress_fem_2pk * stretch
stress_analytic = _get_analytic_stress(stretch, coef, exp)
fig, (ax_stress, ax_difference) = plt.subplots(nrows=2, sharex=True)
ax_stress.plot(stretch, stress_fem, '.-', label='FEM')
ax_stress.plot(stretch, stress_analytic, '--', label='analytic')
ax_difference.plot(stretch, stress_fem - stress_analytic, '.-')
ax_stress.legend(loc='best').set_draggable(True)
ax_stress.set_ylabel(r'nominal stress $\mathrm{[Pa]}$')
ax_stress.grid()
ax_difference.set_ylabel(r'difference in nominal stress $\mathrm{[Pa]}$')
ax_difference.set_xlabel(r'stretch $\mathrm{[-]}$')
ax_difference.grid()
plt.tight_layout()
plt.show()
def stress_strain(
out, problem, _state, order=1, global_stress=None,
global_displacement=None, **_):
"""
Compute the stress and the strain and add them to the output.
Parameters
----------
out : dict
Holds the results of the finite element computation.
problem : sfepy.discrete.Problem
order : int
The approximation order of the displacement field.
global_displacement
Total displacement for each time step, current value will be appended.
global_stress
The true (Cauchy) stress for each time step, current value will be
appended.
Returns
-------
out : dict
"""
strain = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='strain', copy_materials=False)
out['green_strain'] = Struct(
name='output_data', mode='cell', data=strain, dofs=None)
stress_1 = problem.evaluate(
'dw_tl_he_genyeoh.%d.Omega(m1.par, v, u)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress_p = problem.evaluate(
'dw_tl_bulk_pressure.%d.Omega(v, u, p)' % (2*order),
mode='el_avg', term_mode='stress', copy_materials=False)
stress = stress_1 + stress_p
out['stress'] = Struct(
name='output_data', mode='cell', data=stress, dofs=None)
global_stress.append(stress[0, 0, 0, 0])
global_displacement.append(get_displacement(
problem.ts, np.array([[1., 0, 0]]))[0])
return out
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]),
'n_step' : int(ts_vals[2])}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(
dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict([
[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args(
'fu', np.float64, 'scalar', omega, approx_order=order-1)
vector_field = Field.from_args(
'fv', np.float64, 'vector', omega, approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
coefficient, exponent = material_parameters
m_1 = Material(
'm1', par=[coefficient, exponent],
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC(
'displacement', regions['Right'], {'u.0' : disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2*order+1)
term_1 = Term.new(
'dw_tl_he_genyeoh(m1.par, v, u)',
integral, omega, m1=m_1, v=v, u=u)
term_pressure = Term.new(
'dw_tl_bulk_pressure(v, u, p)',
integral, omega, v=v, u=u, p=p)
term_volume_change = Term.new(
'dw_tl_volume(q, u)',
integral, omega, q=q, u=u, term_mode='volume')
term_volume = Term.new(
'dw_volume_integrate(q)',
integral, omega, q=q)
eq_balance = Equation('balance', term_1 + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = Equations([eq_balance, eq_volume])
### Solvers ###
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton(
{'i_max' : 20},
lin_solver=ls, status=nls_status
)
### Problem ###
pb = Problem('hyper', equations=equations)
pb.set_bcs(ebcs=ebcs)
pb.set_ics(ics=Conditions([]))
tss = | SimpleTimeSteppingSolver(ts, nls=nls, context=pb) | sfepy.solvers.ts_solvers.SimpleTimeSteppingSolver |