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from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = | FieldVariable('u-1', 'unknown', field) | sfepy.discrete.FieldVariable |
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = | FieldVariable('u%d' % ii, 'unknown', field) | sfepy.discrete.FieldVariable |
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = | TimeStepper(0.0, 1.0, 1.0, 5) | sfepy.solvers.ts.TimeStepper |
"""
Basic uniform mesh refinement functions.
"""
import numpy as nm
from sfepy.discrete.fem import Mesh
def refine_2_3(mesh_in):
"""
Refines mesh out of triangles by cutting cutting each edge in half
and making 4 new finer triangles out of one coarser one.
"""
cmesh = mesh_in.cmesh
# Unique edge centres.
e_centres = cmesh.get_centroids(cmesh.dim - 1)
# New coordinates after the original ones.
coors = nm.r_[mesh_in.coors, e_centres]
o1 = mesh_in.n_nod
cc = cmesh.get_conn(cmesh.dim, cmesh.dim - 1)
conn = mesh_in.get_conn('2_3')
n_el = conn.shape[0]
e_nodes = cc.indices.reshape((n_el, 3)) + o1
c = nm.c_[conn, e_nodes].T
new_conn = nm.vstack([c[0], c[3], c[5],
c[3], c[4], c[5],
c[1], c[4], c[3],
c[2], c[5], c[4]]).T
new_conn = new_conn.reshape((4 * n_el, 3))
new_mat_id = cmesh.cell_groups.repeat(4)
mesh = Mesh.from_data(mesh_in.name + '_r', coors, None, [new_conn],
[new_mat_id], mesh_in.descs )
return mesh
def refine_2_4(mesh_in):
"""
Refines mesh out of quadrilaterals by cutting cutting each edge in
half and making 4 new finer quadrilaterals out of one coarser one.
"""
cmesh = mesh_in.cmesh
# Unique edge centres.
e_centres = cmesh.get_centroids(cmesh.dim - 1)
# Unique element centres.
centres = cmesh.get_centroids(cmesh.dim)
# New coordinates after the original ones.
coors = nm.r_[mesh_in.coors, e_centres, centres]
o1 = mesh_in.n_nod
o2 = o1 + e_centres.shape[0]
cc = cmesh.get_conn(cmesh.dim, cmesh.dim - 1)
conn = mesh_in.get_conn('2_4')
n_el = conn.shape[0]
e_nodes = cc.indices.reshape((n_el, 4)) + o1
nodes = nm.arange(n_el) + o2
c = nm.c_[conn, e_nodes, nodes].T
new_conn = nm.vstack([c[0], c[4], c[8], c[7],
c[1], c[5], c[8], c[4],
c[2], c[6], c[8], c[5],
c[3], c[7], c[8], c[6]]).T
new_conn = new_conn.reshape((4 * n_el, 4))
new_mat_id = cmesh.cell_groups.repeat(4)
mesh = Mesh.from_data(mesh_in.name + '_r', coors, None, [new_conn],
[new_mat_id], mesh_in.descs )
return mesh
def refine_3_4(mesh_in):
"""
Refines tetrahedra by cutting each edge in half and making 8 new
finer tetrahedra out of one coarser one. Old nodal coordinates come
first in `coors`, then the new ones. The new tetrahedra are similar
to the old one, no degeneration is supposed to occur as at most 3
congruence classes of tetrahedra appear, even when re-applied
iteratively (provided that `conns` are not modified between two
applications - ordering of vertices in tetrahedra matters not only
for positivity of volumes).
References:
- <NAME>: Simplicial grid refinement: on Freudenthal s algorithm and
the optimal number of congruence classes, Numer.Math. 85 (2000),
no. 1, 1--29, or
- <NAME>: Tetrahedral grid refinement, Computing 55 (1995),
no. 4, 355--378, or
http://citeseer.ist.psu.edu/bey95tetrahedral.html
"""
cmesh = mesh_in.cmesh
# Unique edge centres.
e_centres = cmesh.get_centroids(cmesh.dim - 2)
# New coordinates after the original ones.
coors = nm.r_[mesh_in.coors, e_centres]
o1 = mesh_in.n_nod
cc = cmesh.get_conn(cmesh.dim, cmesh.dim - 2)
conn = mesh_in.get_conn('3_4')
n_el = conn.shape[0]
e_nodes = cc.indices.reshape((n_el, 6)) + o1
c = nm.c_[conn, e_nodes].T
new_conn = nm.vstack([c[0], c[4], c[6], c[7],
c[4], c[1], c[5], c[8],
c[6], c[5], c[2], c[9],
c[7], c[8], c[9], c[3],
c[4], c[6], c[7], c[8],
c[4], c[6], c[8], c[5],
c[6], c[7], c[8], c[9],
c[6], c[5], c[9], c[8]]).T
new_conn = new_conn.reshape((8 * n_el, 4))
new_mat_id = cmesh.cell_groups.repeat(8)
mesh = Mesh.from_data(mesh_in.name + '_r', coors, None, [new_conn],
[new_mat_id], mesh_in.descs )
return mesh
def refine_3_8(mesh_in):
"""
Refines hexahedral mesh by cutting cutting each edge in half and
making 8 new finer hexahedrons out of one coarser one.
"""
cmesh = mesh_in.cmesh
# Unique edge centres.
e_centres = cmesh.get_centroids(cmesh.dim - 2)
# Unique face centres.
f_centres = cmesh.get_centroids(cmesh.dim - 1)
# Unique element centres.
centres = cmesh.get_centroids(cmesh.dim)
# New coordinates after the original ones.
coors = nm.r_[mesh_in.coors, e_centres, f_centres, centres]
o1 = mesh_in.n_nod
o2 = o1 + e_centres.shape[0]
o3 = o2 + f_centres.shape[0]
ecc = cmesh.get_conn(cmesh.dim, cmesh.dim - 2)
fcc = cmesh.get_conn(cmesh.dim, cmesh.dim - 1)
conn = mesh_in.get_conn('3_8')
n_el = conn.shape[0]
st = nm.vstack
e_nodes = ecc.indices.reshape((n_el, 12)) + o1
f_nodes = fcc.indices.reshape((n_el, 6)) + o2
nodes = nm.arange(n_el) + o3
c = nm.c_[conn, e_nodes, f_nodes, nodes].T
new_conn = st([c[0], c[8], c[20], c[11], c[16], c[22], c[26], c[21],
c[1], c[9], c[20], c[8], c[17], c[24], c[26], c[22],
c[2], c[10], c[20], c[9], c[18], c[25], c[26], c[24],
c[3], c[11], c[20], c[10], c[19], c[21], c[26], c[25],
c[4], c[15], c[23], c[12], c[16], c[21], c[26], c[22],
c[5], c[12], c[23], c[13], c[17], c[22], c[26], c[24],
c[6], c[13], c[23], c[14], c[18], c[24], c[26], c[25],
c[7], c[14], c[23], c[15], c[19], c[25], c[26], c[21]]).T
new_conn = new_conn.reshape((8 * n_el, 8))
new_mat_id = cmesh.cell_groups.repeat(8)
mesh = Mesh.from_data(mesh_in.name + '_r', coors, None, [new_conn],
[new_mat_id], mesh_in.descs )
return mesh
def refine_reference(geometry, level):
"""
Refine reference element given by `geometry`.
Notes
-----
The error edges must be generated in the order of the connectivity
of the previous (lower) level.
"""
from sfepy.discrete.fem import FEDomain
from sfepy.discrete.fem.geometry_element import geometry_data
gcoors, gconn = geometry.coors, geometry.conn
if level == 0:
return gcoors, gconn, None
gd = geometry_data[geometry.name]
conn = nm.array([gd.conn], dtype=nm.int32)
mat_id = conn[:, 0].copy()
mat_id[:] = 0
mesh = Mesh.from_data('aux', gd.coors, None, [conn],
[mat_id], [geometry.name])
domain = | FEDomain('aux', mesh) | sfepy.discrete.fem.FEDomain |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
| assert_(1 <= dim <= 3) | sfepy.base.base.assert_ |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
| output('generating %d vertices...' % n_nod, verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
| output('...done', verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
| output('generating %d cells...' % n_el, verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
| output('...done', verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = | Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc]) | sfepy.discrete.fem.mesh.Mesh.from_data |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
| output('generating %d vertices...' % n_nod, verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
| assert_(ii == n_nod) | sfepy.base.base.assert_ |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
| output('...done', verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
| output('generating %d cells...' % n_el, verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in | cycle([nr-1, nnfi, nl-1]) | sfepy.linalg.cycle |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
| output('...done', verbose=verbose) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = | Mesh.from_data(name, coors, None, [conn], [mat_id], [desc]) | sfepy.discrete.fem.mesh.Mesh.from_data |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = | match_grid_plane(coors[s1], coors[s2], idim) | sfepy.discrete.fem.periodic.match_grid_plane |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
| output('repeating %s ...' % grid) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
| output('...done') | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
| assert_(kind == 'cube') | sfepy.base.base.assert_ |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
| output(args) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
| ensure_path(filename) | sfepy.base.ioutils.ensure_path |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
| output('creating new cube mesh') | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
| output('to file %s...' % filename) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
| output('...done') | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
| ensure_path(filename) | sfepy.base.ioutils.ensure_path |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
ensure_path(filename)
output('creating new sphere mesh (%i nodes, r=%.2f) and gradation %d'
% args)
| output('to file %s...' % filename) | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
ensure_path(filename)
output('creating new sphere mesh (%i nodes, r=%.2f) and gradation %d'
% args)
output('to file %s...' % filename)
f = open(os.path.join(defdir, 'quantum', 'sphere.geo'))
tmp_dir = tempfile.mkdtemp()
tmpfile = os.path.join(tmp_dir, 'sphere.geo.temp')
ff = open(tmpfile, "w")
ff.write("""
R = %i.0;
n = %i.0;
dens = %f;
""" % args)
ff.write(f.read())
f.close()
ff.close()
subprocess.call(['gmsh', '-3', tmpfile, '-format', 'mesh',
'-o', filename])
shutil.rmtree(tmp_dir)
| output('...done') | sfepy.base.base.output |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
ensure_path(filename)
output('creating new sphere mesh (%i nodes, r=%.2f) and gradation %d'
% args)
output('to file %s...' % filename)
f = open(os.path.join(defdir, 'quantum', 'sphere.geo'))
tmp_dir = tempfile.mkdtemp()
tmpfile = os.path.join(tmp_dir, 'sphere.geo.temp')
ff = open(tmpfile, "w")
ff.write("""
R = %i.0;
n = %i.0;
dens = %f;
""" % args)
ff.write(f.read())
f.close()
ff.close()
subprocess.call(['gmsh', '-3', tmpfile, '-format', 'mesh',
'-o', filename])
shutil.rmtree(tmp_dir)
output('...done')
return filename
def gen_mesh_from_string(mesh_name, mesh_dir):
import re
result = re.match('^\\s*([a-zA-Z]+)[:\\(]([^\\):]*)[:\\)](\\*)?\\s*$',
mesh_name)
if result is None:
return mesh_name
else:
args = re.split(',', result.group(2))
kind = result.group(1)
return gen_misc_mesh(mesh_dir, result.group(3)=='*', kind, args)
def gen_mesh_from_geom(geo, a=None, verbose=False, refine=False):
"""
Runs mesh generator - tetgen for 3D or triangle for 2D meshes.
Parameters
----------
geo : geometry
geometry description
a : int, optional
a maximum area/volume constraint
verbose : bool, optional
detailed information
refine : bool, optional
refines mesh
Returns
-------
mesh : Mesh instance
triangular or tetrahedral mesh
"""
import os.path as op
import pexpect
import tempfile
import shutil
tmp_dir = tempfile.mkdtemp()
polyfilename = op.join(tmp_dir, 'meshgen.poly')
# write geometry to poly file
geo.to_poly_file(polyfilename)
meshgen_call = {2: ('triangle', ''), 3: ('tetgen', 'BFENk')}
params = "-ACp"
params += "q" if refine else ''
params += "V" if verbose else "Q"
params += meshgen_call[geo.dim][1]
if a is not None:
params += "a%f" % (a)
params += " %s" % (polyfilename)
cmd = "%s %s" % (meshgen_call[geo.dim][0], params)
if verbose: print("Generating mesh using", cmd)
p=pexpect.run(cmd, timeout=None)
bname, ext = op.splitext(polyfilename)
if geo.dim == 2:
mesh = | Mesh.from_file(bname + '.1.node') | sfepy.discrete.fem.mesh.Mesh.from_file |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
ensure_path(filename)
output('creating new sphere mesh (%i nodes, r=%.2f) and gradation %d'
% args)
output('to file %s...' % filename)
f = open(os.path.join(defdir, 'quantum', 'sphere.geo'))
tmp_dir = tempfile.mkdtemp()
tmpfile = os.path.join(tmp_dir, 'sphere.geo.temp')
ff = open(tmpfile, "w")
ff.write("""
R = %i.0;
n = %i.0;
dens = %f;
""" % args)
ff.write(f.read())
f.close()
ff.close()
subprocess.call(['gmsh', '-3', tmpfile, '-format', 'mesh',
'-o', filename])
shutil.rmtree(tmp_dir)
output('...done')
return filename
def gen_mesh_from_string(mesh_name, mesh_dir):
import re
result = re.match('^\\s*([a-zA-Z]+)[:\\(]([^\\):]*)[:\\)](\\*)?\\s*$',
mesh_name)
if result is None:
return mesh_name
else:
args = re.split(',', result.group(2))
kind = result.group(1)
return gen_misc_mesh(mesh_dir, result.group(3)=='*', kind, args)
def gen_mesh_from_geom(geo, a=None, verbose=False, refine=False):
"""
Runs mesh generator - tetgen for 3D or triangle for 2D meshes.
Parameters
----------
geo : geometry
geometry description
a : int, optional
a maximum area/volume constraint
verbose : bool, optional
detailed information
refine : bool, optional
refines mesh
Returns
-------
mesh : Mesh instance
triangular or tetrahedral mesh
"""
import os.path as op
import pexpect
import tempfile
import shutil
tmp_dir = tempfile.mkdtemp()
polyfilename = op.join(tmp_dir, 'meshgen.poly')
# write geometry to poly file
geo.to_poly_file(polyfilename)
meshgen_call = {2: ('triangle', ''), 3: ('tetgen', 'BFENk')}
params = "-ACp"
params += "q" if refine else ''
params += "V" if verbose else "Q"
params += meshgen_call[geo.dim][1]
if a is not None:
params += "a%f" % (a)
params += " %s" % (polyfilename)
cmd = "%s %s" % (meshgen_call[geo.dim][0], params)
if verbose: print("Generating mesh using", cmd)
p=pexpect.run(cmd, timeout=None)
bname, ext = op.splitext(polyfilename)
if geo.dim == 2:
mesh = Mesh.from_file(bname + '.1.node')
if geo.dim == 3:
mesh = | Mesh.from_file(bname + '.1.vtk') | sfepy.discrete.fem.mesh.Mesh.from_file |
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
import sys
from six.moves import range
sys.path.append('.')
from sfepy.base.base import output, assert_
from sfepy.base.ioutils import ensure_path
from sfepy.linalg import cycle
from sfepy.discrete.fem.mesh import Mesh
from sfepy.mesh.mesh_tools import elems_q2t
def get_tensor_product_conn(shape):
"""
Generate vertex connectivity for cells of a tensor-product mesh of the
given shape.
Parameters
----------
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the mesh.
Returns
-------
conn : array
The vertex connectivity array.
desc : str
The cell kind.
"""
shape = nm.asarray(shape)
dim = len(shape)
assert_(1 <= dim <= 3)
n_nod = nm.prod(shape)
n_el = nm.prod(shape - 1)
grid = nm.arange(n_nod, dtype=nm.int32)
grid.shape = shape
if dim == 1:
conn = nm.zeros((n_el, 2), dtype=nm.int32)
conn[:, 0] = grid[:-1]
conn[:, 1] = grid[1:]
desc = '1_2'
elif dim == 2:
conn = nm.zeros((n_el, 4), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1].flat
conn[:, 1] = grid[1:, :-1].flat
conn[:, 2] = grid[1:, 1:].flat
conn[:, 3] = grid[:-1, 1:].flat
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
conn[:, 0] = grid[:-1, :-1, :-1].flat
conn[:, 1] = grid[1:, :-1, :-1].flat
conn[:, 2] = grid[1:, 1:, :-1].flat
conn[:, 3] = grid[:-1, 1:, :-1].flat
conn[:, 4] = grid[:-1, :-1, 1:].flat
conn[:, 5] = grid[1:, :-1, 1:].flat
conn[:, 6] = grid[1:, 1:, 1:].flat
conn[:, 7] = grid[:-1, 1:, 1:].flat
desc = '3_8'
return conn, desc
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def _spread_along_axis(axis, coors, tangents, grading_fun):
"""
Spread the coordinates along the given axis using the grading function, and
the tangents in the other two directions.
"""
oo = list(set([0, 1, 2]).difference([axis]))
c0, c1, c2 = coors[:, axis], coors[:, oo[0]], coors[:, oo[1]]
out = nm.empty_like(coors)
mi, ma = c0.min(), c0.max()
nc0 = (c0 - mi) / (ma - mi)
out[:, axis] = oc0 = grading_fun(nc0) * (ma - mi) + mi
nc = oc0 - oc0.min()
mi, ma = c1.min(), c1.max()
n1 = 2 * (c1 - mi) / (ma - mi) - 1
out[:, oo[0]] = c1 + n1 * nc * tangents[oo[0]]
mi, ma = c2.min(), c2.max()
n2 = 2 * (c2 - mi) / (ma - mi) - 1
out[:, oo[1]] = c2 + n2 * nc * tangents[oo[1]]
return out
def _get_extension_side(side, grading_fun, mat_id,
b_dims, b_shape, e_dims, e_shape, centre):
"""
Get a mesh extending the given side of a block mesh.
"""
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
coff = 0.5 * (b_dims + pe_dims)
cc = centre + coff * nm.eye(3)[side]
if side == 0: # x axis.
dims = [pe_dims[0], b_dims[1], b_dims[2]]
shape = [e_shape, b_shape[1], b_shape[2]]
tangents = [0, pe_dims[1] / pe_dims[0], pe_dims[2] / pe_dims[0]]
elif side == 1: # y axis.
dims = [b_dims[0], pe_dims[1], b_dims[2]]
shape = [b_shape[0], e_shape, b_shape[2]]
tangents = [pe_dims[0] / pe_dims[1], 0, pe_dims[2] / pe_dims[1]]
elif side == 2: # z axis.
dims = [b_dims[0], b_dims[1], pe_dims[2]]
shape = [b_shape[0], b_shape[1], e_shape]
tangents = [pe_dims[0] / pe_dims[2], pe_dims[1] / pe_dims[2], 0]
e_mesh = gen_block_mesh(dims, shape, cc, mat_id=mat_id, verbose=False)
e_mesh.coors[:] = _spread_along_axis(side, e_mesh.coors, tangents,
grading_fun)
return e_mesh, shape
def gen_extended_block_mesh(b_dims, b_shape, e_dims, e_shape, centre,
grading_fun=None, name=None):
"""
Generate a 3D mesh with a central block and (coarse) extending side meshes.
The resulting mesh is again a block. Each of the components has a different
material id.
Parameters
----------
b_dims : array of 3 floats
The dimensions of the central block.
b_shape : array of 3 ints
The shape (counts of nodes in x, y, z) of the central block mesh.
e_dims : array of 3 floats
The dimensions of the complete block (central block + extensions).
e_shape : int
The count of nodes of extending blocks in the direction from the
central block.
centre : array of 3 floats
The centre of the mesh.
grading_fun : callable, optional
A function of :math:`x \in [0, 1]` that can be used to shift nodes in
the extension axis directions to allow smooth grading of element sizes
from the centre. The default function is :math:`x**p` with :math:`p`
determined so that the element sizes next to the central block have the
size of the shortest edge of the central block.
name : string, optional
The mesh name.
Returns
-------
mesh : Mesh instance
"""
b_dims = nm.asarray(b_dims, dtype=nm.float64)
b_shape = nm.asarray(b_shape, dtype=nm.int32)
e_dims = nm.asarray(e_dims, dtype=nm.float64)
centre = nm.asarray(centre, dtype=nm.float64)
# Pure extension dimensions.
pe_dims = 0.5 * (e_dims - b_dims)
# Central block element sizes.
dd = (b_dims / (b_shape - 1))
# The "first x" going to grading_fun.
nc = 1.0 / (e_shape - 1)
# Grading power and function.
power = nm.log(dd.min() / pe_dims.min()) / nm.log(nc)
grading_fun = (lambda x: x**power) if grading_fun is None else grading_fun
# Central block mesh.
b_mesh = gen_block_mesh(b_dims, b_shape, centre, mat_id=0, verbose=False)
# 'x' extension.
e_mesh, xs = _get_extension_side(0, grading_fun, 10,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = b_mesh + e_mesh
# Mirror by 'x'.
e_mesh.coors[:, 0] = (2 * centre[0]) - e_mesh.coors[:, 0]
e_mesh.cmesh.cell_groups.fill(11)
mesh = mesh + e_mesh
# 'y' extension.
e_mesh, ys = _get_extension_side(1, grading_fun, 20,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'y'.
e_mesh.coors[:, 1] = (2 * centre[1]) - e_mesh.coors[:, 1]
e_mesh.cmesh.cell_groups.fill(21)
mesh = mesh + e_mesh
# 'z' extension.
e_mesh, zs = _get_extension_side(2, grading_fun, 30,
b_dims, b_shape, e_dims, e_shape, centre)
mesh = mesh + e_mesh
# Mirror by 'z'.
e_mesh.coors[:, 2] = (2 * centre[2]) - e_mesh.coors[:, 2]
e_mesh.cmesh.cell_groups.fill(31)
mesh = mesh + e_mesh
if name is not None:
mesh.name = name
# Verify merging by checking the number of nodes.
n_nod = (nm.prod(nm.maximum(b_shape - 2, 0)) + 2 * nm.prod(xs)
+ 2 * (max(ys[0] - 2, 0) * ys[1] * ys[2])
+ 2 * (max(zs[0] - 2, 0) * max(zs[1] - 2, 0) * zs[2]))
if n_nod != mesh.n_nod:
raise ValueError('Merge of meshes failed! (%d == %d)'
% (n_nod, mesh.n_nod))
return mesh
def tiled_mesh1d(conn, coors, ngrps, idim, n_rep, bb, eps=1e-6, ndmap=False):
from sfepy.discrete.fem.periodic import match_grid_plane
s1 = nm.nonzero(coors[:,idim] < (bb[0] + eps))[0]
s2 = nm.nonzero(coors[:,idim] > (bb[1] - eps))[0]
if s1.shape != s2.shape:
raise ValueError('incompatible shapes: %s == %s'\
% (s1.shape, s2.shape))
(nnod0, dim) = coors.shape
nnod = nnod0 * n_rep - s1.shape[0] * (n_rep - 1)
(nel0, nnel) = conn.shape
nel = nel0 * n_rep
dd = nm.zeros((dim,), dtype=nm.float64)
dd[idim] = bb[1] - bb[0]
m1, m2 = match_grid_plane(coors[s1], coors[s2], idim)
oconn = nm.zeros((nel, nnel), dtype=nm.int32)
ocoors = nm.zeros((nnod, dim), dtype=nm.float64)
ongrps = nm.zeros((nnod,), dtype=nm.int32)
if type(ndmap) is bool:
ret_ndmap = ndmap
else:
ret_ndmap= True
ndmap_out = nm.zeros((nnod,), dtype=nm.int32)
el_off = 0
nd_off = 0
for ii in range(n_rep):
if ii == 0:
oconn[0:nel0,:] = conn
ocoors[0:nnod0,:] = coors
ongrps[0:nnod0] = ngrps.squeeze()
nd_off += nnod0
mapto = s2[m2]
mask = nm.ones((nnod0,), dtype=nm.int32)
mask[s1] = 0
remap0 = nm.cumsum(mask) - 1
nnod0r = nnod0 - s1.shape[0]
cidx = nm.where(mask)
if ret_ndmap:
ndmap_out[0:nnod0] = nm.arange(nnod0)
else:
remap = remap0 + nd_off
remap[s1[m1]] = mapto
mapto = remap[s2[m2]]
ocoors[nd_off:(nd_off + nnod0r),:] =\
(coors[cidx,:] + ii * dd)
ongrps[nd_off:(nd_off + nnod0r)] = ngrps[cidx].squeeze()
oconn[el_off:(el_off + nel0),:] = remap[conn]
if ret_ndmap:
ndmap_out[nd_off:(nd_off + nnod0r)] = cidx[0]
nd_off += nnod0r
el_off += nel0
if ret_ndmap:
if ndmap is not None:
max_nd_ref = nm.max(ndmap)
idxs = nm.where(ndmap_out > max_nd_ref)
ndmap_out[idxs] = ndmap[ndmap_out[idxs]]
return oconn, ocoors, ongrps, ndmap_out
else:
return oconn, ocoors, ongrps
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_misc_mesh(mesh_dir, force_create, kind, args, suffix='.mesh',
verbose=False):
"""
Create sphere or cube mesh according to `kind` in the given
directory if it does not exist and return path to it.
"""
import os
from sfepy import data_dir
defdir = os.path.join(data_dir, 'meshes')
if mesh_dir is None:
mesh_dir = defdir
def retype(args, types, defaults):
args=list(args)
args.extend(defaults[len(args):len(defaults)])
return tuple([type(value) for type, value in zip(types, args) ])
if kind == 'sphere':
default = [5, 41, args[0]]
args = retype(args, [float, int, float], default)
mesh_pattern = os.path.join(mesh_dir, 'sphere-%.2f-%.2f-%i')
else:
assert_(kind == 'cube')
args = retype(args,
(int, float, int, float, int, float),
(args[0], args[1], args[0], args[1], args[0], args[1]))
mesh_pattern = os.path.join(mesh_dir, 'cube-%i_%.2f-%i_%.2f-%i_%.2f')
if verbose:
output(args)
filename = mesh_pattern % args
if not force_create:
if os.path.exists(filename): return filename
if os.path.exists(filename + '.mesh') : return filename + '.mesh'
if os.path.exists(filename + '.vtk'): return filename + '.vtk'
if kind == 'cube':
filename = filename + suffix
ensure_path(filename)
output('creating new cube mesh')
output('(%i nodes in %.2f) x (%i nodes in %.2f) x (%i nodes in %.2f)'
% args)
output('to file %s...' % filename)
mesh = gen_block_mesh(args[1::2], args[0::2],
(0.0, 0.0, 0.0), name=filename)
mesh.write(filename, io='auto')
output('...done')
else:
import subprocess, shutil, tempfile
filename = filename + '.mesh'
ensure_path(filename)
output('creating new sphere mesh (%i nodes, r=%.2f) and gradation %d'
% args)
output('to file %s...' % filename)
f = open(os.path.join(defdir, 'quantum', 'sphere.geo'))
tmp_dir = tempfile.mkdtemp()
tmpfile = os.path.join(tmp_dir, 'sphere.geo.temp')
ff = open(tmpfile, "w")
ff.write("""
R = %i.0;
n = %i.0;
dens = %f;
""" % args)
ff.write(f.read())
f.close()
ff.close()
subprocess.call(['gmsh', '-3', tmpfile, '-format', 'mesh',
'-o', filename])
shutil.rmtree(tmp_dir)
output('...done')
return filename
def gen_mesh_from_string(mesh_name, mesh_dir):
import re
result = re.match('^\\s*([a-zA-Z]+)[:\\(]([^\\):]*)[:\\)](\\*)?\\s*$',
mesh_name)
if result is None:
return mesh_name
else:
args = re.split(',', result.group(2))
kind = result.group(1)
return gen_misc_mesh(mesh_dir, result.group(3)=='*', kind, args)
def gen_mesh_from_geom(geo, a=None, verbose=False, refine=False):
"""
Runs mesh generator - tetgen for 3D or triangle for 2D meshes.
Parameters
----------
geo : geometry
geometry description
a : int, optional
a maximum area/volume constraint
verbose : bool, optional
detailed information
refine : bool, optional
refines mesh
Returns
-------
mesh : Mesh instance
triangular or tetrahedral mesh
"""
import os.path as op
import pexpect
import tempfile
import shutil
tmp_dir = tempfile.mkdtemp()
polyfilename = op.join(tmp_dir, 'meshgen.poly')
# write geometry to poly file
geo.to_poly_file(polyfilename)
meshgen_call = {2: ('triangle', ''), 3: ('tetgen', 'BFENk')}
params = "-ACp"
params += "q" if refine else ''
params += "V" if verbose else "Q"
params += meshgen_call[geo.dim][1]
if a is not None:
params += "a%f" % (a)
params += " %s" % (polyfilename)
cmd = "%s %s" % (meshgen_call[geo.dim][0], params)
if verbose: print("Generating mesh using", cmd)
p=pexpect.run(cmd, timeout=None)
bname, ext = op.splitext(polyfilename)
if geo.dim == 2:
mesh = Mesh.from_file(bname + '.1.node')
if geo.dim == 3:
mesh = Mesh.from_file(bname + '.1.vtk')
shutil.rmtree(tmp_dir)
return mesh
def gen_mesh_from_voxels(voxels, dims, etype='q'):
"""
Generate FE mesh from voxels (volumetric data).
Parameters
----------
voxels : array
Voxel matrix, 1=material.
dims : array
Size of one voxel.
etype : integer, optional
'q' - quadrilateral or hexahedral elements
't' - triangular or tetrahedral elements
Returns
-------
mesh : Mesh instance
Finite element mesh.
"""
dims = nm.array(dims).squeeze()
dim = len(dims)
nddims = nm.array(voxels.shape) + 2
nodemtx = nm.zeros(nddims, dtype=nm.int32)
if dim == 2:
#iy, ix = nm.where(voxels.transpose())
iy, ix = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy] += 1
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 1
nodemtx[ix,iy + 1] += 1
elif etype == 't':
nodemtx[ix,iy] += 2
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 2
nodemtx[ix,iy + 1] += 1
nel *= 2
elif dim == 3:
#iy, ix, iz = nm.where(voxels.transpose(1, 0, 2))
iy, ix, iz = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy,iz] += 1
nodemtx[ix + 1,iy,iz] += 1
nodemtx[ix + 1,iy + 1,iz] += 1
nodemtx[ix,iy + 1,iz] += 1
nodemtx[ix,iy,iz + 1] += 1
nodemtx[ix + 1,iy,iz + 1] += 1
nodemtx[ix + 1,iy + 1,iz + 1] += 1
nodemtx[ix,iy + 1,iz + 1] += 1
elif etype == 't':
nodemtx[ix,iy,iz] += 6
nodemtx[ix + 1,iy,iz] += 2
nodemtx[ix + 1,iy + 1,iz] += 2
nodemtx[ix,iy + 1,iz] += 2
nodemtx[ix,iy,iz + 1] += 2
nodemtx[ix + 1,iy,iz + 1] += 2
nodemtx[ix + 1,iy + 1,iz + 1] += 6
nodemtx[ix,iy + 1,iz + 1] += 2
nel *= 6
else:
msg = 'incorrect voxel dimension! (%d)' % dim
raise ValueError(msg)
ndidx = nm.where(nodemtx)
coors = nm.array(ndidx).transpose() * dims
nnod = coors.shape[0]
nodeid = -nm.ones(nddims, dtype=nm.int32)
nodeid[ndidx] = nm.arange(nnod)
# generate elements
if dim == 2:
elems = nm.array([nodeid[ix,iy],
nodeid[ix + 1,iy],
nodeid[ix + 1,iy + 1],
nodeid[ix,iy + 1]]).transpose()
elif dim == 3:
elems = nm.array([nodeid[ix,iy,iz],
nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix,iy + 1,iz],
nodeid[ix,iy,iz + 1],
nodeid[ix + 1,iy,iz + 1],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz + 1]]).transpose()
if etype == 't':
elems = | elems_q2t(elems) | sfepy.mesh.mesh_tools.elems_q2t |
# 30.05.2007, c
# last revision: 25.02.2008
from __future__ import absolute_import
from sfepy import data_dir
import six
filename_mesh = data_dir + '/meshes/2d/square_unit_tri.mesh'
material_1 = {
'name' : 'coef',
'values' : {
'val' : 1.0,
},
}
material_2 = {
'name' : 'm',
'values' : {
'K' : [[1.0, 0.0], [0.0, 1.0]],
},
}
field_1 = {
'name' : 'a_harmonic_field',
'dtype' : 'real',
'shape' : 'scalar',
'region' : 'Omega',
'approx_order' : 2,
}
variable_1 = {
'name' : 't',
'kind' : 'unknown field',
'field' : 'a_harmonic_field',
'order' : 0,
}
variable_2 = {
'name' : 's',
'kind' : 'test field',
'field' : 'a_harmonic_field',
'dual' : 't',
}
region_1000 = {
'name' : 'Omega',
'select' : 'all',
}
region_1 = {
'name' : 'Left',
'select' : 'vertices in (x < -0.499)',
'kind' : 'facet',
}
region_2 = {
'name' : 'Right',
'select' : 'vertices in (x > 0.499)',
'kind' : 'facet',
}
region_3 = {
'name' : 'Gamma',
'select' : 'vertices of surface',
'kind' : 'facet',
}
ebc_1 = {
'name' : 't_left',
'region' : 'Left',
'dofs' : {'t.0' : 5.0},
}
ebc_2 = {
'name' : 't_right',
'region' : 'Right',
'dofs' : {'t.0' : 0.0},
}
# 'Left' : ('T3', (30,), 'linear_y'),
integral_1 = {
'name' : 'i',
'order' : 2,
}
equations = {
'Temperature' : """dw_laplace.i.Omega( coef.val, s, t ) = 0"""
}
solution = {
't' : '- 5.0 * (x - 0.5)',
}
solver_0 = {
'name' : 'ls',
'kind' : 'ls.scipy_direct',
}
solver_1 = {
'name' : 'newton',
'kind' : 'nls.newton',
'i_max' : 1,
'eps_a' : 1e-10,
}
lin_min, lin_max = 0.0, 2.0
##
# 31.05.2007, c
def linear( bc, ts, coor, which ):
vals = coor[:,which]
min_val, max_val = vals.min(), vals.max()
vals = (vals - min_val) / (max_val - min_val) * (lin_max - lin_min) + lin_min
return vals
##
# 31.05.2007, c
def linear_x( bc, ts, coor ):
return linear( bc, ts, coor, 0 )
def linear_y( bc, ts, coor ):
return linear( bc, ts, coor, 1 )
def linear_z( bc, ts, coor ):
return linear( bc, ts, coor, 2 )
from sfepy.base.testing import TestCommon
##
# 30.05.2007, c
class Test( TestCommon ):
##
# 30.05.2007, c
def from_conf( conf, options ):
from sfepy.applications import solve_pde
problem, state = | solve_pde(conf, save_results=False) | sfepy.applications.solve_pde |
# 30.05.2007, c
# last revision: 25.02.2008
from __future__ import absolute_import
from sfepy import data_dir
import six
filename_mesh = data_dir + '/meshes/2d/square_unit_tri.mesh'
material_1 = {
'name' : 'coef',
'values' : {
'val' : 1.0,
},
}
material_2 = {
'name' : 'm',
'values' : {
'K' : [[1.0, 0.0], [0.0, 1.0]],
},
}
field_1 = {
'name' : 'a_harmonic_field',
'dtype' : 'real',
'shape' : 'scalar',
'region' : 'Omega',
'approx_order' : 2,
}
variable_1 = {
'name' : 't',
'kind' : 'unknown field',
'field' : 'a_harmonic_field',
'order' : 0,
}
variable_2 = {
'name' : 's',
'kind' : 'test field',
'field' : 'a_harmonic_field',
'dual' : 't',
}
region_1000 = {
'name' : 'Omega',
'select' : 'all',
}
region_1 = {
'name' : 'Left',
'select' : 'vertices in (x < -0.499)',
'kind' : 'facet',
}
region_2 = {
'name' : 'Right',
'select' : 'vertices in (x > 0.499)',
'kind' : 'facet',
}
region_3 = {
'name' : 'Gamma',
'select' : 'vertices of surface',
'kind' : 'facet',
}
ebc_1 = {
'name' : 't_left',
'region' : 'Left',
'dofs' : {'t.0' : 5.0},
}
ebc_2 = {
'name' : 't_right',
'region' : 'Right',
'dofs' : {'t.0' : 0.0},
}
# 'Left' : ('T3', (30,), 'linear_y'),
integral_1 = {
'name' : 'i',
'order' : 2,
}
equations = {
'Temperature' : """dw_laplace.i.Omega( coef.val, s, t ) = 0"""
}
solution = {
't' : '- 5.0 * (x - 0.5)',
}
solver_0 = {
'name' : 'ls',
'kind' : 'ls.scipy_direct',
}
solver_1 = {
'name' : 'newton',
'kind' : 'nls.newton',
'i_max' : 1,
'eps_a' : 1e-10,
}
lin_min, lin_max = 0.0, 2.0
##
# 31.05.2007, c
def linear( bc, ts, coor, which ):
vals = coor[:,which]
min_val, max_val = vals.min(), vals.max()
vals = (vals - min_val) / (max_val - min_val) * (lin_max - lin_min) + lin_min
return vals
##
# 31.05.2007, c
def linear_x( bc, ts, coor ):
return linear( bc, ts, coor, 0 )
def linear_y( bc, ts, coor ):
return linear( bc, ts, coor, 1 )
def linear_z( bc, ts, coor ):
return linear( bc, ts, coor, 2 )
from sfepy.base.testing import TestCommon
##
# 30.05.2007, c
class Test( TestCommon ):
##
# 30.05.2007, c
def from_conf( conf, options ):
from sfepy.applications import solve_pde
problem, state = solve_pde(conf, save_results=False)
test = Test(problem=problem, state=state, conf=conf, options=options)
return test
from_conf = staticmethod( from_conf )
##
# 30.05.2007, c
def test_solution( self ):
sol = self.conf.solution
vec = self.state()
problem = self.problem
variables = problem.get_variables()
ok = True
for var_name, expression in six.iteritems(sol):
coor = variables[var_name].field.get_coor()
ana_sol = self.eval_coor_expression( expression, coor )
num_sol = variables.get_state_part_view( vec, var_name )
ret = self.compare_vectors( ana_sol, num_sol,
label1 = 'analytical %s' % var_name,
label2 = 'numerical %s' % var_name )
if not ret:
self.report( 'variable %s: failed' % var_name )
ok = ok and ret
return ok
##
# c: 30.05.2007, r: 19.02.2008
def test_boundary_fluxes( self ):
import os.path as op
from sfepy.linalg import rotation_matrix2d
from sfepy.discrete.evaluate import BasicEvaluator
from sfepy.discrete import Material
problem = self.problem
angles = [0, 30, 45]
region_names = ['Left', 'Right', 'Gamma']
values = [5.0, -5.0, 0.0]
variables = problem.get_variables()
get_state = variables.get_state_part_view
state = self.state.copy(deep=True)
problem.time_update(ebcs={}, epbcs={})
# problem.save_ebc( 'aux.vtk' )
state.apply_ebc()
ev = BasicEvaluator( problem )
aux = ev.eval_residual(state())
field = variables['t'].field
conf_m = problem.conf.get_item_by_name('materials', 'm')
m = | Material.from_conf(conf_m, problem.functions) | sfepy.discrete.Material.from_conf |
# 30.05.2007, c
# last revision: 25.02.2008
from __future__ import absolute_import
from sfepy import data_dir
import six
filename_mesh = data_dir + '/meshes/2d/square_unit_tri.mesh'
material_1 = {
'name' : 'coef',
'values' : {
'val' : 1.0,
},
}
material_2 = {
'name' : 'm',
'values' : {
'K' : [[1.0, 0.0], [0.0, 1.0]],
},
}
field_1 = {
'name' : 'a_harmonic_field',
'dtype' : 'real',
'shape' : 'scalar',
'region' : 'Omega',
'approx_order' : 2,
}
variable_1 = {
'name' : 't',
'kind' : 'unknown field',
'field' : 'a_harmonic_field',
'order' : 0,
}
variable_2 = {
'name' : 's',
'kind' : 'test field',
'field' : 'a_harmonic_field',
'dual' : 't',
}
region_1000 = {
'name' : 'Omega',
'select' : 'all',
}
region_1 = {
'name' : 'Left',
'select' : 'vertices in (x < -0.499)',
'kind' : 'facet',
}
region_2 = {
'name' : 'Right',
'select' : 'vertices in (x > 0.499)',
'kind' : 'facet',
}
region_3 = {
'name' : 'Gamma',
'select' : 'vertices of surface',
'kind' : 'facet',
}
ebc_1 = {
'name' : 't_left',
'region' : 'Left',
'dofs' : {'t.0' : 5.0},
}
ebc_2 = {
'name' : 't_right',
'region' : 'Right',
'dofs' : {'t.0' : 0.0},
}
# 'Left' : ('T3', (30,), 'linear_y'),
integral_1 = {
'name' : 'i',
'order' : 2,
}
equations = {
'Temperature' : """dw_laplace.i.Omega( coef.val, s, t ) = 0"""
}
solution = {
't' : '- 5.0 * (x - 0.5)',
}
solver_0 = {
'name' : 'ls',
'kind' : 'ls.scipy_direct',
}
solver_1 = {
'name' : 'newton',
'kind' : 'nls.newton',
'i_max' : 1,
'eps_a' : 1e-10,
}
lin_min, lin_max = 0.0, 2.0
##
# 31.05.2007, c
def linear( bc, ts, coor, which ):
vals = coor[:,which]
min_val, max_val = vals.min(), vals.max()
vals = (vals - min_val) / (max_val - min_val) * (lin_max - lin_min) + lin_min
return vals
##
# 31.05.2007, c
def linear_x( bc, ts, coor ):
return linear( bc, ts, coor, 0 )
def linear_y( bc, ts, coor ):
return linear( bc, ts, coor, 1 )
def linear_z( bc, ts, coor ):
return linear( bc, ts, coor, 2 )
from sfepy.base.testing import TestCommon
##
# 30.05.2007, c
class Test( TestCommon ):
##
# 30.05.2007, c
def from_conf( conf, options ):
from sfepy.applications import solve_pde
problem, state = solve_pde(conf, save_results=False)
test = Test(problem=problem, state=state, conf=conf, options=options)
return test
from_conf = staticmethod( from_conf )
##
# 30.05.2007, c
def test_solution( self ):
sol = self.conf.solution
vec = self.state()
problem = self.problem
variables = problem.get_variables()
ok = True
for var_name, expression in six.iteritems(sol):
coor = variables[var_name].field.get_coor()
ana_sol = self.eval_coor_expression( expression, coor )
num_sol = variables.get_state_part_view( vec, var_name )
ret = self.compare_vectors( ana_sol, num_sol,
label1 = 'analytical %s' % var_name,
label2 = 'numerical %s' % var_name )
if not ret:
self.report( 'variable %s: failed' % var_name )
ok = ok and ret
return ok
##
# c: 30.05.2007, r: 19.02.2008
def test_boundary_fluxes( self ):
import os.path as op
from sfepy.linalg import rotation_matrix2d
from sfepy.discrete.evaluate import BasicEvaluator
from sfepy.discrete import Material
problem = self.problem
angles = [0, 30, 45]
region_names = ['Left', 'Right', 'Gamma']
values = [5.0, -5.0, 0.0]
variables = problem.get_variables()
get_state = variables.get_state_part_view
state = self.state.copy(deep=True)
problem.time_update(ebcs={}, epbcs={})
# problem.save_ebc( 'aux.vtk' )
state.apply_ebc()
ev = BasicEvaluator( problem )
aux = ev.eval_residual(state())
field = variables['t'].field
conf_m = problem.conf.get_item_by_name('materials', 'm')
m = Material.from_conf(conf_m, problem.functions)
name = op.join( self.options.out_dir,
op.split( problem.domain.mesh.name )[1] + '_%02d.mesh' )
orig_coors = problem.get_mesh_coors().copy()
ok = True
for ia, angle in enumerate( angles ):
self.report( '%d: mesh rotation %d degrees' % (ia, angle) )
problem.domain.mesh.transform_coors( rotation_matrix2d( angle ),
ref_coors = orig_coors )
problem.set_mesh_coors(problem.domain.mesh.coors,
update_fields=True)
problem.domain.mesh.write( name % angle, io = 'auto' )
for ii, region_name in enumerate( region_names ):
flux_term = 'd_surface_flux.i.%s( m.K, t )' % region_name
val1 = problem.evaluate(flux_term, t=variables['t'], m=m)
rvec = get_state( aux, 't', True )
reg = problem.domain.regions[region_name]
nods = field.get_dofs_in_region(reg, merge=True)
val2 = rvec[nods].sum() # Assume 1 dof per node.
ok = ok and ((abs( val1 - values[ii] ) < 1e-10) and
(abs( val2 - values[ii] ) < 1e-10))
self.report( ' %d. %s: %e == %e == %e'\
% (ii, region_name, val1, val2, values[ii]) )
# Restore original coordinates.
problem.domain.mesh.transform_coors( | rotation_matrix2d(0) | sfepy.linalg.rotation_matrix2d |
import numpy as nm
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson
from sfepy.discrete.fem.meshio import UserMeshIO
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy import data_dir
def mesh_hook(mesh, mode):
if mode == 'read':
mesh = gen_block_mesh([0.0098, 0.0011, 0.1], [5, 3, 17],
[0, 0, 0.05], name='specimen',
verbose=False)
return mesh
elif mode == 'write':
pass
def optimization_hook(pb):
cnf = pb.conf
out = []
yield pb, out
state = out[-1][1].get_parts()
coors = pb.domain.cmesh.coors
displ = state['u'].reshape((coors.shape[0],3))
# elongation
mcoors = coors[cnf.mnodes, 2]
mdispl = displ[cnf.mnodes, 2]
dl = (mdispl[1] - mdispl[0]) / (mcoors[1] - mcoors[0])
if hasattr(cnf, 'opt_data'):
# compute slope of the force-elongation curve
cnf.opt_data['k'] = cnf.F / dl
yield None
def get_mat(coors, mode, pb):
if mode == 'qp':
# get material data
if hasattr(pb.conf, 'opt_data'):
# from homogenization
D = pb.conf.opt_data['D_homog']
else:
# given values
D = stiffness_from_youngpoisson(3, 150.0e9, 0.3)
nqp = coors.shape[0]
return {'D': nm.tile(D, (nqp, 1, 1))}
def define(is_opt=False):
filename_mesh = | UserMeshIO(mesh_hook) | sfepy.discrete.fem.meshio.UserMeshIO |
import numpy as nm
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson
from sfepy.discrete.fem.meshio import UserMeshIO
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy import data_dir
def mesh_hook(mesh, mode):
if mode == 'read':
mesh = gen_block_mesh([0.0098, 0.0011, 0.1], [5, 3, 17],
[0, 0, 0.05], name='specimen',
verbose=False)
return mesh
elif mode == 'write':
pass
def optimization_hook(pb):
cnf = pb.conf
out = []
yield pb, out
state = out[-1][1].get_parts()
coors = pb.domain.cmesh.coors
displ = state['u'].reshape((coors.shape[0],3))
# elongation
mcoors = coors[cnf.mnodes, 2]
mdispl = displ[cnf.mnodes, 2]
dl = (mdispl[1] - mdispl[0]) / (mcoors[1] - mcoors[0])
if hasattr(cnf, 'opt_data'):
# compute slope of the force-elongation curve
cnf.opt_data['k'] = cnf.F / dl
yield None
def get_mat(coors, mode, pb):
if mode == 'qp':
# get material data
if hasattr(pb.conf, 'opt_data'):
# from homogenization
D = pb.conf.opt_data['D_homog']
else:
# given values
D = | stiffness_from_youngpoisson(3, 150.0e9, 0.3) | sfepy.mechanics.matcoefs.stiffness_from_youngpoisson |
# -*- coding: utf-8 -*-
"""
Fields for Discontinous Galerkin method
"""
import numpy as nm
import six
from numpy.lib.stride_tricks import as_strided
from six.moves import range
from sfepy.base.base import (output, assert_, Struct)
from sfepy.discrete import Integral, PolySpace
from sfepy.discrete.common.fields import parse_shape
from sfepy.discrete.fem.fields_base import FEField
from sfepy.discrete.fem.mappings import VolumeMapping
def get_unraveler(n_el_nod, n_cell):
"""Returns function for unraveling i.e. unpacking dof data from
serialized array from shape (n_el_nod*n_cell, 1) to (n_cell, n_el_nod, 1).
The unraveler returns non-writeable view into the input array.
Parameters
----------
n_el_nod : int
expected dimensions of dofs array
n_cell : int
Returns
-------
unravel : callable
"""
def unravel(u):
"""Returns non-writeable view into the input array reshaped to
(n*m, 1) to (m, n, 1) .
Parameters
----------
u : array_like
solution in shape (n*m, 1)
Returns
-------
u : ndarray
unraveledsolution in shape (m, n, 1)
"""
ustride1 = u.strides[0]
ur = as_strided(u,
shape=(n_cell, n_el_nod, 1),
strides=(n_el_nod * ustride1, ustride1, ustride1),
writeable=False)
return ur
return unravel
def get_raveler(n_el_nod, n_cell):
"""Returns function for raveling i.e. packing dof data from
two dimensional array of shape (n_cell, n_el_nod, 1) to (n_el_nod*n_cell, 1)
The raveler returns view into the input array.
Parameters
----------
n_el_nod :
param n_el_nod, n_cell: expected dimensions of dofs array
n_cell : int
Returns
-------
ravel : callable
"""
def ravel(u):
"""Returns view into the input array reshaped from (m, n, 1) to (n*m, 1)
to (m, n, 1) .
Parameters
----------
u : array_like
Returns
-------
u : ndarray
"""
# ustride1 = u.strides[0]
# ur = as_strided(u, shape=(n_el_nod*n_cell, 1),
# strides=(n_cell*ustride1, ustride1))
ur = nm.ravel(u)[:, None]
# possibly use according to
# https://docs.scipy.org/doc/numpy/reference/generated/numpy.ravel.html
# ur = u.reshape(-1)
return ur
return ravel
# mapping between geometry element types
# and their facets types
# TODO move to sfepy/discrete/fem/geometry_element.py?
cell_facet_gel_name = {
"1_2": "0_1",
"2_3": "1_2",
"2_4": "1_2",
"3_4": "2_3",
"3_8": "2_4"
}
def get_gel(region):
"""
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
gel :
base geometry element of the region
"""
cmesh = region.domain.cmesh
for key, gel in six.iteritems(region.domain.geom_els):
ct = cmesh.cell_types
if (ct[region.cells] == cmesh.key_to_index[gel.name]).all():
return gel
else:
raise ValueError('Region {} contains multiple'
' reference geometries!'.format(region))
class DGField(FEField):
"""Class for usage with DG terms, provides functionality for Discontinous
Galerkin method like neighbour look up, projection to discontinuous basis
and correct DOF treatment.
"""
family_name = 'volume_DG_legendre_discontinuous'
is_surface = False
def __init__(self, name, dtype, shape, region, space="H1",
poly_space_base="legendre", approx_order=1, integral=None):
"""
Creates DGField, with Legendre polyspace and default integral
corresponding to 2 * approx_order.
Parameters
----------
name : string
dtype : type
shape : string
'vector', 'scalar' or something else
region : sfepy.discrete.common.region.Region
space : string
default "H1"
poly_space_base : PolySpace
optionally force polyspace
approx_order : 0 for FVM, default 1
integral : Integral
if None integral of order 2*approx_order is created
"""
shape = | parse_shape(shape, region.domain.shape.dim) | sfepy.discrete.common.fields.parse_shape |
# -*- coding: utf-8 -*-
"""
Fields for Discontinous Galerkin method
"""
import numpy as nm
import six
from numpy.lib.stride_tricks import as_strided
from six.moves import range
from sfepy.base.base import (output, assert_, Struct)
from sfepy.discrete import Integral, PolySpace
from sfepy.discrete.common.fields import parse_shape
from sfepy.discrete.fem.fields_base import FEField
from sfepy.discrete.fem.mappings import VolumeMapping
def get_unraveler(n_el_nod, n_cell):
"""Returns function for unraveling i.e. unpacking dof data from
serialized array from shape (n_el_nod*n_cell, 1) to (n_cell, n_el_nod, 1).
The unraveler returns non-writeable view into the input array.
Parameters
----------
n_el_nod : int
expected dimensions of dofs array
n_cell : int
Returns
-------
unravel : callable
"""
def unravel(u):
"""Returns non-writeable view into the input array reshaped to
(n*m, 1) to (m, n, 1) .
Parameters
----------
u : array_like
solution in shape (n*m, 1)
Returns
-------
u : ndarray
unraveledsolution in shape (m, n, 1)
"""
ustride1 = u.strides[0]
ur = as_strided(u,
shape=(n_cell, n_el_nod, 1),
strides=(n_el_nod * ustride1, ustride1, ustride1),
writeable=False)
return ur
return unravel
def get_raveler(n_el_nod, n_cell):
"""Returns function for raveling i.e. packing dof data from
two dimensional array of shape (n_cell, n_el_nod, 1) to (n_el_nod*n_cell, 1)
The raveler returns view into the input array.
Parameters
----------
n_el_nod :
param n_el_nod, n_cell: expected dimensions of dofs array
n_cell : int
Returns
-------
ravel : callable
"""
def ravel(u):
"""Returns view into the input array reshaped from (m, n, 1) to (n*m, 1)
to (m, n, 1) .
Parameters
----------
u : array_like
Returns
-------
u : ndarray
"""
# ustride1 = u.strides[0]
# ur = as_strided(u, shape=(n_el_nod*n_cell, 1),
# strides=(n_cell*ustride1, ustride1))
ur = nm.ravel(u)[:, None]
# possibly use according to
# https://docs.scipy.org/doc/numpy/reference/generated/numpy.ravel.html
# ur = u.reshape(-1)
return ur
return ravel
# mapping between geometry element types
# and their facets types
# TODO move to sfepy/discrete/fem/geometry_element.py?
cell_facet_gel_name = {
"1_2": "0_1",
"2_3": "1_2",
"2_4": "1_2",
"3_4": "2_3",
"3_8": "2_4"
}
def get_gel(region):
"""
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
gel :
base geometry element of the region
"""
cmesh = region.domain.cmesh
for key, gel in six.iteritems(region.domain.geom_els):
ct = cmesh.cell_types
if (ct[region.cells] == cmesh.key_to_index[gel.name]).all():
return gel
else:
raise ValueError('Region {} contains multiple'
' reference geometries!'.format(region))
class DGField(FEField):
"""Class for usage with DG terms, provides functionality for Discontinous
Galerkin method like neighbour look up, projection to discontinuous basis
and correct DOF treatment.
"""
family_name = 'volume_DG_legendre_discontinuous'
is_surface = False
def __init__(self, name, dtype, shape, region, space="H1",
poly_space_base="legendre", approx_order=1, integral=None):
"""
Creates DGField, with Legendre polyspace and default integral
corresponding to 2 * approx_order.
Parameters
----------
name : string
dtype : type
shape : string
'vector', 'scalar' or something else
region : sfepy.discrete.common.region.Region
space : string
default "H1"
poly_space_base : PolySpace
optionally force polyspace
approx_order : 0 for FVM, default 1
integral : Integral
if None integral of order 2*approx_order is created
"""
shape = parse_shape(shape, region.domain.shape.dim)
Struct.__init__(self, name=name, dtype=dtype, shape=shape,
region=region)
if isinstance(approx_order, tuple):
self.approx_order = approx_order[0]
else:
self.approx_order = approx_order
# geometry
self.domain = region.domain
self.region = region
self.dim = region.tdim
self._setup_geometry()
self._setup_connectivity()
# TODO treat domains embedded into higher dimensional spaces?
self.n_el_facets = self.dim + 1 if self.gel.is_simplex else 2**self.dim
# approximation space
self.space = space
self.poly_space_base = poly_space_base
self.force_bubble = False
self._create_interpolant()
# DOFs
self._setup_shape()
self._setup_all_dofs()
self.ravel_sol = get_raveler(self.n_el_nod, self.n_cell)
self.unravel_sol = get_unraveler(self.n_el_nod, self.n_cell)
# integral
self.clear_qp_base()
self.clear_facet_qp_base()
if integral is None:
self.integral = Integral("dg_fi", order = 2 * self.approx_order)
else:
self.integral = integral
self.ori = None
self.basis_transform = None
# mapping
self.mappings = {}
self.mapping = self.create_mapping(self.region, self.integral, "volume",
return_mapping=True)[1]
self.mappings0 = {}
# neighbour facet mapping and data caches
# TODO use lru cache or different method?
self.clear_facet_neighbour_idx_cache()
self.clear_normals_cache()
self.clear_facet_vols_cache()
self.boundary_facet_local_idx = {}
def _create_interpolant(self):
name = self.gel.name + '_DG_legendre'
ps = PolySpace.any_from_args(name, self.gel, self.approx_order,
base=self.poly_space_base,
force_bubble=False)
self.poly_space = ps
# 'legendre_simplex' is created for '1_2'.
if self.gel.name in ["2_4", "3_8"]:
self.extended = True
else:
self.extended = False
def _setup_all_dofs(self):
"""Sets up all the differet kinds of DOFs, for DG only bubble DOFs"""
self.n_el_nod = self.poly_space.n_nod
self.n_vertex_dof = 0 # in DG we will propably never need vertex DOFs
self.n_edge_dof = 0 # use facets DOFS for AFS methods
self.n_face_dof = 0 # use facet DOF for AFS methods
(self.n_bubble_dof,
self.bubble_remap,
self.bubble_dofs) = self._setup_bubble_dofs()
self.n_nod = self.n_vertex_dof + self.n_edge_dof \
+ self.n_face_dof + self.n_bubble_dof
def _setup_bubble_dofs(self):
"""Creates DOF information for so called element, cell or bubble DOFs
- the only DOFs used in DG
n_dof = n_cells * n_el_nod
remap optional remapping between cells
dofs is mapping between dofs and cells
Returns
-------
n_dof : int
remap : ndarray
dofs : ndarray
"""
self.n_cell = self.region.get_n_cells(self.is_surface)
n_dof = self.n_cell * self.n_el_nod
dofs = nm.arange(n_dof, dtype=nm.int32)\
.reshape(self.n_cell, self.n_el_nod)
remap = nm.arange(self.n_cell)
self.econn = dofs
self.dofs2cells = nm.repeat(nm.arange(self.n_cell), self.n_el_nod)
return n_dof, remap, dofs
def _setup_shape(self):
"""What is shape used for and what it really means.
Does it represent shape of the problem?
"""
self.n_components = nm.prod(self.shape)
self.val_shape = self.shape
def _setup_geometry(self):
"""Setup the field region geometry."""
# get_gel extracts the highest dimension geometry from self.region
self.gel = get_gel(self.region)
def _setup_connectivity(self):
"""Forces self.domain.mesh to build necessary conductivities
so they are available in self.get_nbrhd_dofs
"""
self.region.domain.mesh.cmesh.setup_connectivity(self.dim, self.dim)
self.region.domain.mesh.cmesh.setup_connectivity(self.dim - 1, self.dim)
self.region.domain.mesh.cmesh.setup_connectivity(self.dim, self.dim - 1)
def get_coor(self, nods=None):
"""Returns coors for matching nodes
# TODO revise DG_EPBC and EPBC matching?
Parameters
----------
nods :
if None use all nodes (Default value = None)
Returns
-------
coors : ndarray
coors on surface
"""
if nods is None:
nods = self.bubble_dofs
cells = self.dofs2cells[nods]
coors = self.domain.mesh.cmesh.get_centroids(self.dim)[cells]
eps = min(self.domain.cmesh.get_volumes(self.dim)) / (self.n_el_nod + 2)
if self.dim == 1:
extended_coors = nm.zeros(nm.shape(coors)[:-1] + (2,))
extended_coors[:, 0] = coors[:, 0]
coors = extended_coors
# shift centroid coors to lie within cells but be different for each dof
# use coors of facet QPs?
coors += eps * nm.repeat(nm.arange(self.n_el_nod),
len(nm.unique(cells)))[:, None]
return coors
def clear_facet_qp_base(self):
"""Clears facet_qp_base cache"""
self.facet_bf = {}
self.facet_qp = None
self.facet_whs = None
def _transform_qps_to_facets(self, qps, geo_name):
"""Transforms points given in qps to all facets of the reference element
with geometry geo_name.
Parameters
----------
qps :
qps corresponding to facet dimension to be transformed
geo_name :
element type
Returns
-------
tqps : ndarray
tqps is of shape shape(qps) + (n_el_facets, geo dim)
"""
if geo_name == "1_2":
tqps = nm.zeros(nm.shape(qps) + (2, 1,))
tqps[..., 0, 0] = 0.
tqps[..., 1, 0] = 1.
elif geo_name == "2_3":
tqps = nm.zeros(nm.shape(qps) + (3, 2,))
# 0.
tqps[..., 0, 0] = qps # x = 0 + t
tqps[..., 0, 1] = 0. # y = 0
# 1.
tqps[..., 1, 0] = 1 - qps # x = 1 - t
tqps[..., 1, 1] = qps # y = t
# 2.
tqps[..., 2, 0] = 0 # x = 0
tqps[..., 2, 1] = 1 - qps # y = 1 - t
elif geo_name == "2_4":
tqps = nm.zeros(nm.shape(qps) + (4, 2,))
# 0.
tqps[..., 0, 0] = qps # x = t
tqps[..., 0, 1] = 0. # y = 0
# 1.
tqps[..., 1, 0] = 1 # x = 1
tqps[..., 1, 1] = qps # y = t
# 2.
tqps[..., 2, 0] = 1 - qps # x = 1 -t
tqps[..., 2, 1] = 1 # y = 1
# 3.
tqps[..., 3, 0] = 0 # x = 0
tqps[..., 3, 1] = 1 - qps # y = 1 - t
elif geo_name == "3_4":
# tqps = nm.zeros(nm.shape(qps) + (4, 3,))
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
elif geo_name == "3_8":
# tqps = nm.zeros(nm.shape(qps) + (8, 3,))
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
else:
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
return tqps
def get_facet_qp(self):
"""Returns quadrature points on all facets of the reference element in
array of shape (n_qp, 1 , n_el_facets, dim)
Returns
-------
qps : ndarray
quadrature points
weights : ndarray
Still needs to be transformed to actual facets!
"""
if self.dim == 1:
facet_qps = self._transform_qps_to_facets(nm.zeros((1, 1)), "1_2")
weights = nm.ones((1, 1, 1))
else:
qps, weights = self.integral.get_qp(cell_facet_gel_name[self.gel.name])
weights = weights[None, :, None]
facet_qps = self._transform_qps_to_facets(qps, self.gel.name)
return facet_qps, weights
def get_facet_base(self, derivative=False, base_only=False):
"""
Returns values of base in facets quadrature points, data shape is a bit
crazy right now:
(number of qps, 1, n_el_facets, 1, n_el_nod)
end for derivatine:
(1, number of qps, (dim,) * derivative, n_el_facets, 1, n_el_nod)
Parameters
----------
derivative: truthy or integer
base_only: do not return weights
Returns
-------
facet_bf : ndarray
values of basis functions in facet qps
weights : ndarray, optionally
weights of qps
"""
if derivative:
diff = int(derivative)
else:
diff = 0
if diff in self.facet_bf:
facet_bf = self.facet_bf[diff]
whs = self.facet_whs
else:
qps, whs = self.get_facet_qp()
ps = self.poly_space
self.facet_qp = qps
self.facet_whs = whs
if derivative:
facet_bf = nm.zeros((1,) + nm.shape(qps)[:-1] +
(self.dim,) * diff + (self.n_el_nod,))
else:
facet_bf = nm.zeros(nm.shape(qps)[:-1] + (1, self.n_el_nod,))
for i in range(self.n_el_facets):
facet_bf[..., i, :, :] = \
ps.eval_base(qps[..., i, :], diff=diff,
transform=self.basis_transform)
self.facet_bf[diff] = facet_bf
if base_only:
return facet_bf
else:
return facet_bf, whs
def clear_facet_neighbour_idx_cache(self, region=None):
"""
If region is None clear all!
Parameters
----------
region : sfepy.discrete.common.region.Region
If None clear all.
"""
if region is None:
self.facet_neighbour_index = {}
else:
self.facet_neighbour_index.pop(region.name)
def get_facet_neighbor_idx(self, region=None, eq_map=None):
"""
Returns index of cell neighbours sharing facet, along with local index
of the facet within neighbour, also treats periodic boundary conditions
i.e. plugs correct neighbours for cell on periodic boundary.
Where there are no neighbours specified puts -1 instead of neighbour
and facet id
Cashes neighbour index in self.facet_neighbours
Parameters
----------
region : sfepy.discrete.common.region.Region
Main region, must contain cells.
eq_map :
eq_map from state variable containing information on
EPBC and DG EPBC. (Default value = None)
Returns
-------
facet_neighbours : ndarray
Shape is
(n_cell, n_el_facet, 2),
first value is index of the neighbouring cell,
the second is index of the facet in said nb. cell.
"""
if region is None or eq_map is None:
# HOTFIX enabling limiter to obtain connectivity data without
# knowing eq_map or region
if self.region.name in self.facet_neighbour_index:
return self.facet_neighbour_index[self.region.name]
else:
raise ValueError("No facet neighbour mapping for main " +
"region {}".format(self.region.name) +
" cached yet, call with region and " +
"eq_map first.")
if region.name in self.facet_neighbour_index:
return self.facet_neighbour_index[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
cells = region.cells
facet_neighbours = nm.zeros((n_cell, n_el_facets, 2), dtype=nm.int32)
c2fi, c2fo = cmesh.get_incident(dim - 1, cells, dim, ret_offsets=True)
for ic, o1 in enumerate(c2fo[:-1]): # loop over cells
o2 = c2fo[ic + 1]
# get neighbours per facet of the cell
c2ci, c2co = cmesh.get_incident(dim, c2fi[o1:o2], dim - 1,
ret_offsets=True)
ii = cmesh.get_local_ids(c2fi[o1:o2], dim - 1, c2ci, c2co, dim)
fis = nm.c_[c2ci, ii]
nbrs = []
for ifa, of1 in enumerate(c2co[:-1]): # loop over facets
of2 = c2co[ifa + 1]
if of2 == (of1 + 1): # facet has only one cell
# Surface facet.
nbrs.append([-1, -1]) # c2ci[of1]) # append no neighbours
else:
if c2ci[of1] == cells[ic]: # do not append the cell itself
nbrs.append(fis[of2 - 1])
else:
nbrs.append(fis[of1])
facet_neighbours[ic, :, :] = nbrs
facet_neighbours = \
self._set_fem_periodic_facet_neighbours(facet_neighbours, eq_map)
facet_neighbours = \
self._set_dg_periodic_facet_neighbours(facet_neighbours, eq_map)
# cache results
self.facet_neighbour_index[region.name] = facet_neighbours
return facet_neighbours
def _set_dg_periodic_facet_neighbours(self, facet_neighbours, eq_map):
"""
Parameters
----------
facet_neighbours : array_like
Shape is
(n_cell, n_el_facet, 2),
first value is index of the neighbouring cell
the second is index of the facet in said nb. cell.
eq_map :
must contain dg_ep_bc a List with pairs of slave and master boundary
cell boundary facet mapping
Returns
-------
facet_neighbours : ndarray
Updated incidence array.
"""
# if eq_map.
# treat DG EPBC - these are definitely preferred
if eq_map.n_dg_epbc > 0 and self.gel.name not in ["1_2", "2_4", "3_6"]:
raise ValueError(
"Periodic boundary conditions not supported " +
"for geometry {} elements.".format(self.gel.name))
dg_epbc = eq_map.dg_epbc
for master_bc2bfi, slave_bc2bfi in dg_epbc:
# set neighbours of periodic cells to one another
facet_neighbours[master_bc2bfi[:, 0], master_bc2bfi[:, 1], 0] = \
slave_bc2bfi[:, 0]
facet_neighbours[slave_bc2bfi[:, 0], slave_bc2bfi[:, 1], 0] = \
master_bc2bfi[:, 0]
# set neighbours facets
facet_neighbours[slave_bc2bfi[:, 0], slave_bc2bfi[:, 1], 1] = \
master_bc2bfi[:, 1]
facet_neighbours[master_bc2bfi[:, 0], master_bc2bfi[:, 1], 1] =\
slave_bc2bfi[:, 1]
return facet_neighbours
def _set_fem_periodic_facet_neighbours(self, facet_neighbours, eq_map):
"""Maybe remove after DG EPBC revision in self.get_coor
Parameters
----------
facet_neighbours : array_like
Shape is (n_cell, n_el_facet, 2), first value is index of the
neighbouring cell the second is index of the facet in said nb. cell.
eq_map :
eq_map from state variable containing information on
EPBC and DG EPBC.
Returns
-------
facet_neighbours : ndarray
Updated incidence array.
"""
# treat classical FEM EPBCs - we need to correct neighbours
if eq_map.n_epbc > 0:
# set neighbours of periodic cells to one another
mcells = nm.unique(self.dofs2cells[eq_map.master])
scells = nm.unique(self.dofs2cells[eq_map.slave])
mcells_facets = nm.array(
nm.where(facet_neighbours[mcells] == -1))[1, 0] # facets mcells
scells_facets = nm.array(
nm.where(facet_neighbours[scells] == -1))[1, 0] # facets scells
# [1, 0] above, first we need second axis to get axis on which
# facet indices are stored, second we drop axis with neighbour
# local facet index,
#
# for multiple s/mcells this will have to be
# something like 1 + 2*nm.arange(len(mcells)) - to skip double
# entries for -1 tags in neighbours and neighbour local facet idx
# set neighbours of mcells to scells
facet_neighbours[mcells, mcells_facets, 0] = scells
# set neighbour facets to facets of scell missing neighbour
facet_neighbours[
mcells, mcells_facets, 1] = scells_facets
# we do not need to distinguish EBC and EPBC cells, EBC overwrite
# EPBC, we only need to fix shapes
# set neighbours of scells to mcells
facet_neighbours[scells, scells_facets, 0] = mcells
# set neighbour facets to facets of mcell missing neighbour0
facet_neighbours[
scells, scells_facets, 1] = mcells_facets
return facet_neighbours
@staticmethod
def get_region_info(region):
"""
Extracts information about region needed in various methods of DGField
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
dim, n_cell, n_el_facets
"""
if not region.has_cells():
raise ValueError("Region {} has no cells".format(region.name))
n_cell = region.get_n_cells()
dim = region.tdim
gel = get_gel(region)
n_el_facets = dim + 1 if gel.is_simplex else 2 ** dim
return dim, n_cell, n_el_facets
def get_both_facet_state_vals(self, state, region,
derivative=None, reduce_nod=True):
"""Computes values of the variable represented by dofs in
quadrature points located at facets, returns both values -
inner and outer, along with weights.
Parameters
----------
state : state variable containing BC info
region : sfepy.discrete.common.region.Region
derivative : compute derivative if truthy,
compute n-th derivative if a number (Default value = None)
reduce_nod : if False DOES NOT sum nodes into values at QPs
(Default value = True)
Returns
-------
inner_facet_values (n_cell, n_el_facets, n_qp),
outer facet values (n_cell, n_el_facets, n_qp),
weights,
if derivative is True:
inner_facet_values (n_cell, n_el_facets, dim, n_qp),
outer_facet values (n_cell, n_el_facets, dim, n_qp)
"""
if derivative:
diff = int(derivative)
else:
diff = 0
unreduce_nod = int(not reduce_nod)
inner_base_vals, outer_base_vals, whs = \
self.get_both_facet_base_vals(state, region, derivative=derivative)
dofs = self.unravel_sol(state.data[0])
n_qp = whs.shape[-1]
outputs_shape = (self.n_cell, self.n_el_facets) + \
(self.n_el_nod,) * unreduce_nod + \
(self.dim,) * diff + \
(n_qp,)
inner_facet_vals = nm.zeros(outputs_shape)
if unreduce_nod:
inner_facet_vals[:] = nm.einsum('id...,idf...->ifd...',
dofs, inner_base_vals)
else:
inner_facet_vals[:] = nm.einsum('id...,id...->i...',
dofs, inner_base_vals)
per_facet_neighbours = self.get_facet_neighbor_idx(region, state.eq_map)
outer_facet_vals = nm.zeros(outputs_shape)
for facet_n in range(self.n_el_facets):
if unreduce_nod:
outer_facet_vals[:, facet_n, :] = \
nm.einsum('id...,id...->id...',
dofs[per_facet_neighbours[:, facet_n, 0]],
outer_base_vals[:, :, facet_n])
else:
outer_facet_vals[:, facet_n, :] = \
nm.einsum('id...,id...->i...',
dofs[per_facet_neighbours[:, facet_n, 0]],
outer_base_vals[:, :, facet_n])
boundary_cells = nm.array(nm.where(per_facet_neighbours[:, :, 0] < 0)).T
outer_facet_vals[boundary_cells[:, 0], boundary_cells[:, 1]] = 0.0
# TODO detect and print boundary cells without defined BCs?
for ebc, ebc_vals in zip(state.eq_map.dg_ebc.get(diff, []),
state.eq_map.dg_ebc_val.get(diff, [])):
if unreduce_nod:
raise NotImplementedError(
"Unreduced DOFs are not available for boundary " +
"outerfacets")
outer_facet_vals[ebc[:, 0], ebc[:, 1], :] = \
nm.einsum("id,id...->id...",
ebc_vals, inner_base_vals[0, :, ebc[:, 1]])
else:
# fix flipping qp order to accomodate for
# opposite facet orientation of neighbours
outer_facet_vals[ebc[:, 0], ebc[:, 1], :] = ebc_vals[:, ::-1]
# flip outer_facet_vals moved to get_both_facet_base_vals
return inner_facet_vals, outer_facet_vals, whs
def get_both_facet_base_vals(self, state, region, derivative=None):
"""Returns values of the basis function in quadrature points on facets
broadcasted to all cells inner to the element as well as outer ones
along with weights for the qps broadcasted and transformed to elements.
Contains quick fix to flip facet QPs for right integration order.
Parameters
----------
state : used to get EPBC info
region : sfepy.discrete.common.region.Region for connectivity
derivative : if u need derivative
(Default value = None)
Returns
-------
outer_facet_base_vals:
inner_facet_base_vals:
shape (n_cell, n_el_nod, n_el_facet, n_qp) or
(n_cell, n_el_nod, n_el_facet, dim, n_qp)
when derivative is True or 1
whs: shape (n_cell, n_el_facet, n_qp)
"""
if derivative:
diff = int(derivative)
else:
diff = 0
facet_bf, whs = self.get_facet_base(derivative=derivative)
n_qp = nm.shape(whs)[1]
facet_vols = self.get_facet_vols(region)
whs = facet_vols * whs[None, :, :, 0]
base_shape = (self.n_cell, self.n_el_nod, self.n_el_facets) + \
(self.dim,) * diff + \
(n_qp,)
inner_facet_base_vals = nm.zeros(base_shape)
outer_facet_base_vals = nm.zeros(base_shape)
if derivative:
inner_facet_base_vals[:] = facet_bf[0, :, 0, :, :, :]\
.swapaxes(-2, -3).T
else:
inner_facet_base_vals[:] = facet_bf[:, 0, :, 0, :].T
per_facet_neighbours = self.get_facet_neighbor_idx(region, state.eq_map)
# numpy prepends shape resulting from multiple
# indexing before remaining shape
if derivative:
outer_facet_base_vals[:] = \
inner_facet_base_vals[0, :, per_facet_neighbours[:, :, 1]]\
.swapaxes(-3, -4)
else:
outer_facet_base_vals[:] = \
inner_facet_base_vals[0, :, per_facet_neighbours[:, :, 1]]\
.swapaxes(-2, -3)
# fix to flip facet QPs for right integration order
return inner_facet_base_vals, outer_facet_base_vals[..., ::-1], whs
def clear_normals_cache(self, region=None):
"""Clears normals cache for given region or all regions.
Parameters
----------
region : sfepy.discrete.common.region.Region
region to clear cache or None to clear all
"""
if region is None:
self.normals_cache = {}
else:
if isinstance(region, str):
self.normals_cache.pop(region)
else:
self.normals_cache.pop(region.name)
def get_cell_normals_per_facet(self, region):
"""Caches results, use clear_normals_cache to clear the cache.
Parameters
----------
region: sfepy.discrete.common.region.Region
Main region, must contain cells.
Returns
-------
normals: ndarray
normals of facets in array of shape (n_cell, n_el_facets, dim)
"""
if region.name in self.normals_cache:
return self.normals_cache[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
normals = cmesh.get_facet_normals()
normals_out = nm.zeros((n_cell, n_el_facets, dim))
c2f = cmesh.get_conn(dim, dim - 1)
for ic, o1 in enumerate(c2f.offsets[:-1]):
o2 = c2f.offsets[ic + 1]
for ifal, ifa in enumerate(c2f.indices[o1:o2]):
normals_out[ic, ifal] = normals[o1 + ifal]
self.normals_cache[region.name] = normals_out
return normals_out
def clear_facet_vols_cache(self, region=None):
"""Clears facet volume cache for given region or all regions.
Parameters
----------
region : sfepy.discrete.common.region.Region
region to clear cache or None to clear all
"""
if region is None:
self.facet_vols_cache = {}
else:
if isinstance(region, str):
self.facet_vols_cache.pop(region)
else:
self.facet_vols_cache.pop(region.name)
def get_facet_vols(self, region):
"""Caches results, use clear_facet_vols_cache to clear the cache
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
vols_out: ndarray
volumes of the facets by cells shape (n_cell, n_el_facets, 1)
"""
if region.name in self.facet_vols_cache:
return self.facet_vols_cache[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
if dim == 1:
vols = nm.ones((cmesh.num[0], 1))
else:
vols = cmesh.get_volumes(dim - 1)[:, None]
vols_out = nm.zeros((n_cell, n_el_facets, 1))
c2f = cmesh.get_conn(dim, dim - 1)
for ic, o1 in enumerate(c2f.offsets[:-1]):
o2 = c2f.offsets[ic + 1]
for ifal, ifa in enumerate(c2f.indices[o1:o2]):
vols_out[ic, ifal] = vols[ifa]
self.facet_vols_cache[region.name] = vols_out
return vols_out
def get_data_shape(self, integral, integration='volume', region_name=None):
"""Returns data shape
(n_nod, n_qp, self.gel.dim, self.n_el_nod)
Parameters
----------
integral : integral used
integration :
'volume' is only supported value (Default value = 'volume')
region_name : not used
(Default value = None)
Returns
-------
data_shape : tuple
"""
if integration in ('volume',):
# from FEField.get_data_shape()
_, weights = integral.get_qp(self.gel.name)
n_qp = weights.shape[0]
data_shape = (self.n_cell, n_qp, self.gel.dim, self.n_el_nod)
# econn.shape[1] == n_el_nod i.e. number nod in element
else:
raise NotImplementedError('unsupported integration! (%s)'
% integration)
return data_shape
def get_econn(self, conn_type, region, is_trace=False, integration=None):
"""Getter for econn
Parameters
----------
conn_type : string or Struct
'volume' is only supported
region : sfepy.discrete.common.region.Region
is_trace : ignored
(Default value = False)
integration : ignored
(Default value = None)
Returns
-------
econn : ndarray
connectivity information
"""
ct = conn_type.type if isinstance(conn_type, Struct) else conn_type
if ct == 'volume':
if region.name == self.region.name:
conn = self.econn
else:
raise ValueError("Bad region for the field")
else:
raise ValueError('unknown connectivity type! (%s)' % ct)
return conn
def setup_extra_data(self, geometry, info, is_trace):
"""This is called in create_adof_conns(conn_info, var_indx=None,
active_only=True, verbose=True)
for each variable but has no effect.
Parameters
----------
geometry :
ignored
info :
set to self.info
is_trace :
set to self.trace
"""
# placeholder, what is this used for?
# dct = info.dc_type.type
self.info = info
self.is_trace = is_trace
def get_dofs_in_region(self, region, merge=True):
"""Return indices of DOFs that belong to the given region.
Not Used in BC treatment
Parameters
----------
region : sfepy.discrete.common.region.Region
merge : bool
merge dof tuple into one numpy array, default True
Returns
-------
dofs : ndarray
"""
dofs = []
if region.has_cells(): # main region or its part
els = nm.ravel(self.bubble_remap[region.cells])
eldofs = self.bubble_dofs[els[els >= 0]]
dofs.append(eldofs)
else:
# return indices of cells adjacent to boundary facets
dim = self.dim
cmesh = region.domain.mesh.cmesh
bc_cells = cmesh.get_incident(dim, region.facets, dim - 1)
bc_dofs = self.bubble_dofs[bc_cells]
dofs.append(bc_dofs)
if merge:
dofs = nm.concatenate(dofs)
return dofs
def get_bc_facet_idx(self, region):
"""Caches results in self.boundary_facet_local_idx
Parameters
----------
region : sfepy.discrete.common.region.Region
surface region defining BCs
Returns
-------
bc2bfi : ndarray
index of cells on boundary along with corresponding facets
"""
if region.name in self.boundary_facet_local_idx:
return self.boundary_facet_local_idx[region.name]
bc2bfi = region.get_facet_indices()
self.boundary_facet_local_idx[region.name] = bc2bfi
return bc2bfi
def create_mapping(self, region, integral, integration,
return_mapping=True):
"""Creates and returns mapping
Parameters
----------
region : sfepy.discrete.common.region.Region
integral : Integral
integration : str
'volume' is only accepted option
return_mapping : default True
(Default value = True)
Returns
-------
mapping : VolumeMapping
"""
domain = self.domain
coors = domain.get_mesh_coors(actual=True)
dconn = domain.get_conn()
# from FEField
if integration == 'volume':
qp = self.get_qp('v', integral)
# qp = self.integral.get_qp(self.gel.name)
iels = region.get_cells()
geo_ps = self.gel.poly_space
ps = self.poly_space
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, iels.astype(nm.int32), axis=0)
mapping = | VolumeMapping(coors, conn, poly_space=geo_ps) | sfepy.discrete.fem.mappings.VolumeMapping |
# -*- coding: utf-8 -*-
"""
Fields for Discontinous Galerkin method
"""
import numpy as nm
import six
from numpy.lib.stride_tricks import as_strided
from six.moves import range
from sfepy.base.base import (output, assert_, Struct)
from sfepy.discrete import Integral, PolySpace
from sfepy.discrete.common.fields import parse_shape
from sfepy.discrete.fem.fields_base import FEField
from sfepy.discrete.fem.mappings import VolumeMapping
def get_unraveler(n_el_nod, n_cell):
"""Returns function for unraveling i.e. unpacking dof data from
serialized array from shape (n_el_nod*n_cell, 1) to (n_cell, n_el_nod, 1).
The unraveler returns non-writeable view into the input array.
Parameters
----------
n_el_nod : int
expected dimensions of dofs array
n_cell : int
Returns
-------
unravel : callable
"""
def unravel(u):
"""Returns non-writeable view into the input array reshaped to
(n*m, 1) to (m, n, 1) .
Parameters
----------
u : array_like
solution in shape (n*m, 1)
Returns
-------
u : ndarray
unraveledsolution in shape (m, n, 1)
"""
ustride1 = u.strides[0]
ur = as_strided(u,
shape=(n_cell, n_el_nod, 1),
strides=(n_el_nod * ustride1, ustride1, ustride1),
writeable=False)
return ur
return unravel
def get_raveler(n_el_nod, n_cell):
"""Returns function for raveling i.e. packing dof data from
two dimensional array of shape (n_cell, n_el_nod, 1) to (n_el_nod*n_cell, 1)
The raveler returns view into the input array.
Parameters
----------
n_el_nod :
param n_el_nod, n_cell: expected dimensions of dofs array
n_cell : int
Returns
-------
ravel : callable
"""
def ravel(u):
"""Returns view into the input array reshaped from (m, n, 1) to (n*m, 1)
to (m, n, 1) .
Parameters
----------
u : array_like
Returns
-------
u : ndarray
"""
# ustride1 = u.strides[0]
# ur = as_strided(u, shape=(n_el_nod*n_cell, 1),
# strides=(n_cell*ustride1, ustride1))
ur = nm.ravel(u)[:, None]
# possibly use according to
# https://docs.scipy.org/doc/numpy/reference/generated/numpy.ravel.html
# ur = u.reshape(-1)
return ur
return ravel
# mapping between geometry element types
# and their facets types
# TODO move to sfepy/discrete/fem/geometry_element.py?
cell_facet_gel_name = {
"1_2": "0_1",
"2_3": "1_2",
"2_4": "1_2",
"3_4": "2_3",
"3_8": "2_4"
}
def get_gel(region):
"""
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
gel :
base geometry element of the region
"""
cmesh = region.domain.cmesh
for key, gel in six.iteritems(region.domain.geom_els):
ct = cmesh.cell_types
if (ct[region.cells] == cmesh.key_to_index[gel.name]).all():
return gel
else:
raise ValueError('Region {} contains multiple'
' reference geometries!'.format(region))
class DGField(FEField):
"""Class for usage with DG terms, provides functionality for Discontinous
Galerkin method like neighbour look up, projection to discontinuous basis
and correct DOF treatment.
"""
family_name = 'volume_DG_legendre_discontinuous'
is_surface = False
def __init__(self, name, dtype, shape, region, space="H1",
poly_space_base="legendre", approx_order=1, integral=None):
"""
Creates DGField, with Legendre polyspace and default integral
corresponding to 2 * approx_order.
Parameters
----------
name : string
dtype : type
shape : string
'vector', 'scalar' or something else
region : sfepy.discrete.common.region.Region
space : string
default "H1"
poly_space_base : PolySpace
optionally force polyspace
approx_order : 0 for FVM, default 1
integral : Integral
if None integral of order 2*approx_order is created
"""
shape = parse_shape(shape, region.domain.shape.dim)
Struct.__init__(self, name=name, dtype=dtype, shape=shape,
region=region)
if isinstance(approx_order, tuple):
self.approx_order = approx_order[0]
else:
self.approx_order = approx_order
# geometry
self.domain = region.domain
self.region = region
self.dim = region.tdim
self._setup_geometry()
self._setup_connectivity()
# TODO treat domains embedded into higher dimensional spaces?
self.n_el_facets = self.dim + 1 if self.gel.is_simplex else 2**self.dim
# approximation space
self.space = space
self.poly_space_base = poly_space_base
self.force_bubble = False
self._create_interpolant()
# DOFs
self._setup_shape()
self._setup_all_dofs()
self.ravel_sol = get_raveler(self.n_el_nod, self.n_cell)
self.unravel_sol = get_unraveler(self.n_el_nod, self.n_cell)
# integral
self.clear_qp_base()
self.clear_facet_qp_base()
if integral is None:
self.integral = Integral("dg_fi", order = 2 * self.approx_order)
else:
self.integral = integral
self.ori = None
self.basis_transform = None
# mapping
self.mappings = {}
self.mapping = self.create_mapping(self.region, self.integral, "volume",
return_mapping=True)[1]
self.mappings0 = {}
# neighbour facet mapping and data caches
# TODO use lru cache or different method?
self.clear_facet_neighbour_idx_cache()
self.clear_normals_cache()
self.clear_facet_vols_cache()
self.boundary_facet_local_idx = {}
def _create_interpolant(self):
name = self.gel.name + '_DG_legendre'
ps = PolySpace.any_from_args(name, self.gel, self.approx_order,
base=self.poly_space_base,
force_bubble=False)
self.poly_space = ps
# 'legendre_simplex' is created for '1_2'.
if self.gel.name in ["2_4", "3_8"]:
self.extended = True
else:
self.extended = False
def _setup_all_dofs(self):
"""Sets up all the differet kinds of DOFs, for DG only bubble DOFs"""
self.n_el_nod = self.poly_space.n_nod
self.n_vertex_dof = 0 # in DG we will propably never need vertex DOFs
self.n_edge_dof = 0 # use facets DOFS for AFS methods
self.n_face_dof = 0 # use facet DOF for AFS methods
(self.n_bubble_dof,
self.bubble_remap,
self.bubble_dofs) = self._setup_bubble_dofs()
self.n_nod = self.n_vertex_dof + self.n_edge_dof \
+ self.n_face_dof + self.n_bubble_dof
def _setup_bubble_dofs(self):
"""Creates DOF information for so called element, cell or bubble DOFs
- the only DOFs used in DG
n_dof = n_cells * n_el_nod
remap optional remapping between cells
dofs is mapping between dofs and cells
Returns
-------
n_dof : int
remap : ndarray
dofs : ndarray
"""
self.n_cell = self.region.get_n_cells(self.is_surface)
n_dof = self.n_cell * self.n_el_nod
dofs = nm.arange(n_dof, dtype=nm.int32)\
.reshape(self.n_cell, self.n_el_nod)
remap = nm.arange(self.n_cell)
self.econn = dofs
self.dofs2cells = nm.repeat(nm.arange(self.n_cell), self.n_el_nod)
return n_dof, remap, dofs
def _setup_shape(self):
"""What is shape used for and what it really means.
Does it represent shape of the problem?
"""
self.n_components = nm.prod(self.shape)
self.val_shape = self.shape
def _setup_geometry(self):
"""Setup the field region geometry."""
# get_gel extracts the highest dimension geometry from self.region
self.gel = get_gel(self.region)
def _setup_connectivity(self):
"""Forces self.domain.mesh to build necessary conductivities
so they are available in self.get_nbrhd_dofs
"""
self.region.domain.mesh.cmesh.setup_connectivity(self.dim, self.dim)
self.region.domain.mesh.cmesh.setup_connectivity(self.dim - 1, self.dim)
self.region.domain.mesh.cmesh.setup_connectivity(self.dim, self.dim - 1)
def get_coor(self, nods=None):
"""Returns coors for matching nodes
# TODO revise DG_EPBC and EPBC matching?
Parameters
----------
nods :
if None use all nodes (Default value = None)
Returns
-------
coors : ndarray
coors on surface
"""
if nods is None:
nods = self.bubble_dofs
cells = self.dofs2cells[nods]
coors = self.domain.mesh.cmesh.get_centroids(self.dim)[cells]
eps = min(self.domain.cmesh.get_volumes(self.dim)) / (self.n_el_nod + 2)
if self.dim == 1:
extended_coors = nm.zeros(nm.shape(coors)[:-1] + (2,))
extended_coors[:, 0] = coors[:, 0]
coors = extended_coors
# shift centroid coors to lie within cells but be different for each dof
# use coors of facet QPs?
coors += eps * nm.repeat(nm.arange(self.n_el_nod),
len(nm.unique(cells)))[:, None]
return coors
def clear_facet_qp_base(self):
"""Clears facet_qp_base cache"""
self.facet_bf = {}
self.facet_qp = None
self.facet_whs = None
def _transform_qps_to_facets(self, qps, geo_name):
"""Transforms points given in qps to all facets of the reference element
with geometry geo_name.
Parameters
----------
qps :
qps corresponding to facet dimension to be transformed
geo_name :
element type
Returns
-------
tqps : ndarray
tqps is of shape shape(qps) + (n_el_facets, geo dim)
"""
if geo_name == "1_2":
tqps = nm.zeros(nm.shape(qps) + (2, 1,))
tqps[..., 0, 0] = 0.
tqps[..., 1, 0] = 1.
elif geo_name == "2_3":
tqps = nm.zeros(nm.shape(qps) + (3, 2,))
# 0.
tqps[..., 0, 0] = qps # x = 0 + t
tqps[..., 0, 1] = 0. # y = 0
# 1.
tqps[..., 1, 0] = 1 - qps # x = 1 - t
tqps[..., 1, 1] = qps # y = t
# 2.
tqps[..., 2, 0] = 0 # x = 0
tqps[..., 2, 1] = 1 - qps # y = 1 - t
elif geo_name == "2_4":
tqps = nm.zeros(nm.shape(qps) + (4, 2,))
# 0.
tqps[..., 0, 0] = qps # x = t
tqps[..., 0, 1] = 0. # y = 0
# 1.
tqps[..., 1, 0] = 1 # x = 1
tqps[..., 1, 1] = qps # y = t
# 2.
tqps[..., 2, 0] = 1 - qps # x = 1 -t
tqps[..., 2, 1] = 1 # y = 1
# 3.
tqps[..., 3, 0] = 0 # x = 0
tqps[..., 3, 1] = 1 - qps # y = 1 - t
elif geo_name == "3_4":
# tqps = nm.zeros(nm.shape(qps) + (4, 3,))
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
elif geo_name == "3_8":
# tqps = nm.zeros(nm.shape(qps) + (8, 3,))
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
else:
raise NotImplementedError("Geometry {} not supported, yet"
.format(geo_name))
return tqps
def get_facet_qp(self):
"""Returns quadrature points on all facets of the reference element in
array of shape (n_qp, 1 , n_el_facets, dim)
Returns
-------
qps : ndarray
quadrature points
weights : ndarray
Still needs to be transformed to actual facets!
"""
if self.dim == 1:
facet_qps = self._transform_qps_to_facets(nm.zeros((1, 1)), "1_2")
weights = nm.ones((1, 1, 1))
else:
qps, weights = self.integral.get_qp(cell_facet_gel_name[self.gel.name])
weights = weights[None, :, None]
facet_qps = self._transform_qps_to_facets(qps, self.gel.name)
return facet_qps, weights
def get_facet_base(self, derivative=False, base_only=False):
"""
Returns values of base in facets quadrature points, data shape is a bit
crazy right now:
(number of qps, 1, n_el_facets, 1, n_el_nod)
end for derivatine:
(1, number of qps, (dim,) * derivative, n_el_facets, 1, n_el_nod)
Parameters
----------
derivative: truthy or integer
base_only: do not return weights
Returns
-------
facet_bf : ndarray
values of basis functions in facet qps
weights : ndarray, optionally
weights of qps
"""
if derivative:
diff = int(derivative)
else:
diff = 0
if diff in self.facet_bf:
facet_bf = self.facet_bf[diff]
whs = self.facet_whs
else:
qps, whs = self.get_facet_qp()
ps = self.poly_space
self.facet_qp = qps
self.facet_whs = whs
if derivative:
facet_bf = nm.zeros((1,) + nm.shape(qps)[:-1] +
(self.dim,) * diff + (self.n_el_nod,))
else:
facet_bf = nm.zeros(nm.shape(qps)[:-1] + (1, self.n_el_nod,))
for i in range(self.n_el_facets):
facet_bf[..., i, :, :] = \
ps.eval_base(qps[..., i, :], diff=diff,
transform=self.basis_transform)
self.facet_bf[diff] = facet_bf
if base_only:
return facet_bf
else:
return facet_bf, whs
def clear_facet_neighbour_idx_cache(self, region=None):
"""
If region is None clear all!
Parameters
----------
region : sfepy.discrete.common.region.Region
If None clear all.
"""
if region is None:
self.facet_neighbour_index = {}
else:
self.facet_neighbour_index.pop(region.name)
def get_facet_neighbor_idx(self, region=None, eq_map=None):
"""
Returns index of cell neighbours sharing facet, along with local index
of the facet within neighbour, also treats periodic boundary conditions
i.e. plugs correct neighbours for cell on periodic boundary.
Where there are no neighbours specified puts -1 instead of neighbour
and facet id
Cashes neighbour index in self.facet_neighbours
Parameters
----------
region : sfepy.discrete.common.region.Region
Main region, must contain cells.
eq_map :
eq_map from state variable containing information on
EPBC and DG EPBC. (Default value = None)
Returns
-------
facet_neighbours : ndarray
Shape is
(n_cell, n_el_facet, 2),
first value is index of the neighbouring cell,
the second is index of the facet in said nb. cell.
"""
if region is None or eq_map is None:
# HOTFIX enabling limiter to obtain connectivity data without
# knowing eq_map or region
if self.region.name in self.facet_neighbour_index:
return self.facet_neighbour_index[self.region.name]
else:
raise ValueError("No facet neighbour mapping for main " +
"region {}".format(self.region.name) +
" cached yet, call with region and " +
"eq_map first.")
if region.name in self.facet_neighbour_index:
return self.facet_neighbour_index[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
cells = region.cells
facet_neighbours = nm.zeros((n_cell, n_el_facets, 2), dtype=nm.int32)
c2fi, c2fo = cmesh.get_incident(dim - 1, cells, dim, ret_offsets=True)
for ic, o1 in enumerate(c2fo[:-1]): # loop over cells
o2 = c2fo[ic + 1]
# get neighbours per facet of the cell
c2ci, c2co = cmesh.get_incident(dim, c2fi[o1:o2], dim - 1,
ret_offsets=True)
ii = cmesh.get_local_ids(c2fi[o1:o2], dim - 1, c2ci, c2co, dim)
fis = nm.c_[c2ci, ii]
nbrs = []
for ifa, of1 in enumerate(c2co[:-1]): # loop over facets
of2 = c2co[ifa + 1]
if of2 == (of1 + 1): # facet has only one cell
# Surface facet.
nbrs.append([-1, -1]) # c2ci[of1]) # append no neighbours
else:
if c2ci[of1] == cells[ic]: # do not append the cell itself
nbrs.append(fis[of2 - 1])
else:
nbrs.append(fis[of1])
facet_neighbours[ic, :, :] = nbrs
facet_neighbours = \
self._set_fem_periodic_facet_neighbours(facet_neighbours, eq_map)
facet_neighbours = \
self._set_dg_periodic_facet_neighbours(facet_neighbours, eq_map)
# cache results
self.facet_neighbour_index[region.name] = facet_neighbours
return facet_neighbours
def _set_dg_periodic_facet_neighbours(self, facet_neighbours, eq_map):
"""
Parameters
----------
facet_neighbours : array_like
Shape is
(n_cell, n_el_facet, 2),
first value is index of the neighbouring cell
the second is index of the facet in said nb. cell.
eq_map :
must contain dg_ep_bc a List with pairs of slave and master boundary
cell boundary facet mapping
Returns
-------
facet_neighbours : ndarray
Updated incidence array.
"""
# if eq_map.
# treat DG EPBC - these are definitely preferred
if eq_map.n_dg_epbc > 0 and self.gel.name not in ["1_2", "2_4", "3_6"]:
raise ValueError(
"Periodic boundary conditions not supported " +
"for geometry {} elements.".format(self.gel.name))
dg_epbc = eq_map.dg_epbc
for master_bc2bfi, slave_bc2bfi in dg_epbc:
# set neighbours of periodic cells to one another
facet_neighbours[master_bc2bfi[:, 0], master_bc2bfi[:, 1], 0] = \
slave_bc2bfi[:, 0]
facet_neighbours[slave_bc2bfi[:, 0], slave_bc2bfi[:, 1], 0] = \
master_bc2bfi[:, 0]
# set neighbours facets
facet_neighbours[slave_bc2bfi[:, 0], slave_bc2bfi[:, 1], 1] = \
master_bc2bfi[:, 1]
facet_neighbours[master_bc2bfi[:, 0], master_bc2bfi[:, 1], 1] =\
slave_bc2bfi[:, 1]
return facet_neighbours
def _set_fem_periodic_facet_neighbours(self, facet_neighbours, eq_map):
"""Maybe remove after DG EPBC revision in self.get_coor
Parameters
----------
facet_neighbours : array_like
Shape is (n_cell, n_el_facet, 2), first value is index of the
neighbouring cell the second is index of the facet in said nb. cell.
eq_map :
eq_map from state variable containing information on
EPBC and DG EPBC.
Returns
-------
facet_neighbours : ndarray
Updated incidence array.
"""
# treat classical FEM EPBCs - we need to correct neighbours
if eq_map.n_epbc > 0:
# set neighbours of periodic cells to one another
mcells = nm.unique(self.dofs2cells[eq_map.master])
scells = nm.unique(self.dofs2cells[eq_map.slave])
mcells_facets = nm.array(
nm.where(facet_neighbours[mcells] == -1))[1, 0] # facets mcells
scells_facets = nm.array(
nm.where(facet_neighbours[scells] == -1))[1, 0] # facets scells
# [1, 0] above, first we need second axis to get axis on which
# facet indices are stored, second we drop axis with neighbour
# local facet index,
#
# for multiple s/mcells this will have to be
# something like 1 + 2*nm.arange(len(mcells)) - to skip double
# entries for -1 tags in neighbours and neighbour local facet idx
# set neighbours of mcells to scells
facet_neighbours[mcells, mcells_facets, 0] = scells
# set neighbour facets to facets of scell missing neighbour
facet_neighbours[
mcells, mcells_facets, 1] = scells_facets
# we do not need to distinguish EBC and EPBC cells, EBC overwrite
# EPBC, we only need to fix shapes
# set neighbours of scells to mcells
facet_neighbours[scells, scells_facets, 0] = mcells
# set neighbour facets to facets of mcell missing neighbour0
facet_neighbours[
scells, scells_facets, 1] = mcells_facets
return facet_neighbours
@staticmethod
def get_region_info(region):
"""
Extracts information about region needed in various methods of DGField
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
dim, n_cell, n_el_facets
"""
if not region.has_cells():
raise ValueError("Region {} has no cells".format(region.name))
n_cell = region.get_n_cells()
dim = region.tdim
gel = get_gel(region)
n_el_facets = dim + 1 if gel.is_simplex else 2 ** dim
return dim, n_cell, n_el_facets
def get_both_facet_state_vals(self, state, region,
derivative=None, reduce_nod=True):
"""Computes values of the variable represented by dofs in
quadrature points located at facets, returns both values -
inner and outer, along with weights.
Parameters
----------
state : state variable containing BC info
region : sfepy.discrete.common.region.Region
derivative : compute derivative if truthy,
compute n-th derivative if a number (Default value = None)
reduce_nod : if False DOES NOT sum nodes into values at QPs
(Default value = True)
Returns
-------
inner_facet_values (n_cell, n_el_facets, n_qp),
outer facet values (n_cell, n_el_facets, n_qp),
weights,
if derivative is True:
inner_facet_values (n_cell, n_el_facets, dim, n_qp),
outer_facet values (n_cell, n_el_facets, dim, n_qp)
"""
if derivative:
diff = int(derivative)
else:
diff = 0
unreduce_nod = int(not reduce_nod)
inner_base_vals, outer_base_vals, whs = \
self.get_both_facet_base_vals(state, region, derivative=derivative)
dofs = self.unravel_sol(state.data[0])
n_qp = whs.shape[-1]
outputs_shape = (self.n_cell, self.n_el_facets) + \
(self.n_el_nod,) * unreduce_nod + \
(self.dim,) * diff + \
(n_qp,)
inner_facet_vals = nm.zeros(outputs_shape)
if unreduce_nod:
inner_facet_vals[:] = nm.einsum('id...,idf...->ifd...',
dofs, inner_base_vals)
else:
inner_facet_vals[:] = nm.einsum('id...,id...->i...',
dofs, inner_base_vals)
per_facet_neighbours = self.get_facet_neighbor_idx(region, state.eq_map)
outer_facet_vals = nm.zeros(outputs_shape)
for facet_n in range(self.n_el_facets):
if unreduce_nod:
outer_facet_vals[:, facet_n, :] = \
nm.einsum('id...,id...->id...',
dofs[per_facet_neighbours[:, facet_n, 0]],
outer_base_vals[:, :, facet_n])
else:
outer_facet_vals[:, facet_n, :] = \
nm.einsum('id...,id...->i...',
dofs[per_facet_neighbours[:, facet_n, 0]],
outer_base_vals[:, :, facet_n])
boundary_cells = nm.array(nm.where(per_facet_neighbours[:, :, 0] < 0)).T
outer_facet_vals[boundary_cells[:, 0], boundary_cells[:, 1]] = 0.0
# TODO detect and print boundary cells without defined BCs?
for ebc, ebc_vals in zip(state.eq_map.dg_ebc.get(diff, []),
state.eq_map.dg_ebc_val.get(diff, [])):
if unreduce_nod:
raise NotImplementedError(
"Unreduced DOFs are not available for boundary " +
"outerfacets")
outer_facet_vals[ebc[:, 0], ebc[:, 1], :] = \
nm.einsum("id,id...->id...",
ebc_vals, inner_base_vals[0, :, ebc[:, 1]])
else:
# fix flipping qp order to accomodate for
# opposite facet orientation of neighbours
outer_facet_vals[ebc[:, 0], ebc[:, 1], :] = ebc_vals[:, ::-1]
# flip outer_facet_vals moved to get_both_facet_base_vals
return inner_facet_vals, outer_facet_vals, whs
def get_both_facet_base_vals(self, state, region, derivative=None):
"""Returns values of the basis function in quadrature points on facets
broadcasted to all cells inner to the element as well as outer ones
along with weights for the qps broadcasted and transformed to elements.
Contains quick fix to flip facet QPs for right integration order.
Parameters
----------
state : used to get EPBC info
region : sfepy.discrete.common.region.Region for connectivity
derivative : if u need derivative
(Default value = None)
Returns
-------
outer_facet_base_vals:
inner_facet_base_vals:
shape (n_cell, n_el_nod, n_el_facet, n_qp) or
(n_cell, n_el_nod, n_el_facet, dim, n_qp)
when derivative is True or 1
whs: shape (n_cell, n_el_facet, n_qp)
"""
if derivative:
diff = int(derivative)
else:
diff = 0
facet_bf, whs = self.get_facet_base(derivative=derivative)
n_qp = nm.shape(whs)[1]
facet_vols = self.get_facet_vols(region)
whs = facet_vols * whs[None, :, :, 0]
base_shape = (self.n_cell, self.n_el_nod, self.n_el_facets) + \
(self.dim,) * diff + \
(n_qp,)
inner_facet_base_vals = nm.zeros(base_shape)
outer_facet_base_vals = nm.zeros(base_shape)
if derivative:
inner_facet_base_vals[:] = facet_bf[0, :, 0, :, :, :]\
.swapaxes(-2, -3).T
else:
inner_facet_base_vals[:] = facet_bf[:, 0, :, 0, :].T
per_facet_neighbours = self.get_facet_neighbor_idx(region, state.eq_map)
# numpy prepends shape resulting from multiple
# indexing before remaining shape
if derivative:
outer_facet_base_vals[:] = \
inner_facet_base_vals[0, :, per_facet_neighbours[:, :, 1]]\
.swapaxes(-3, -4)
else:
outer_facet_base_vals[:] = \
inner_facet_base_vals[0, :, per_facet_neighbours[:, :, 1]]\
.swapaxes(-2, -3)
# fix to flip facet QPs for right integration order
return inner_facet_base_vals, outer_facet_base_vals[..., ::-1], whs
def clear_normals_cache(self, region=None):
"""Clears normals cache for given region or all regions.
Parameters
----------
region : sfepy.discrete.common.region.Region
region to clear cache or None to clear all
"""
if region is None:
self.normals_cache = {}
else:
if isinstance(region, str):
self.normals_cache.pop(region)
else:
self.normals_cache.pop(region.name)
def get_cell_normals_per_facet(self, region):
"""Caches results, use clear_normals_cache to clear the cache.
Parameters
----------
region: sfepy.discrete.common.region.Region
Main region, must contain cells.
Returns
-------
normals: ndarray
normals of facets in array of shape (n_cell, n_el_facets, dim)
"""
if region.name in self.normals_cache:
return self.normals_cache[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
normals = cmesh.get_facet_normals()
normals_out = nm.zeros((n_cell, n_el_facets, dim))
c2f = cmesh.get_conn(dim, dim - 1)
for ic, o1 in enumerate(c2f.offsets[:-1]):
o2 = c2f.offsets[ic + 1]
for ifal, ifa in enumerate(c2f.indices[o1:o2]):
normals_out[ic, ifal] = normals[o1 + ifal]
self.normals_cache[region.name] = normals_out
return normals_out
def clear_facet_vols_cache(self, region=None):
"""Clears facet volume cache for given region or all regions.
Parameters
----------
region : sfepy.discrete.common.region.Region
region to clear cache or None to clear all
"""
if region is None:
self.facet_vols_cache = {}
else:
if isinstance(region, str):
self.facet_vols_cache.pop(region)
else:
self.facet_vols_cache.pop(region.name)
def get_facet_vols(self, region):
"""Caches results, use clear_facet_vols_cache to clear the cache
Parameters
----------
region : sfepy.discrete.common.region.Region
Returns
-------
vols_out: ndarray
volumes of the facets by cells shape (n_cell, n_el_facets, 1)
"""
if region.name in self.facet_vols_cache:
return self.facet_vols_cache[region.name]
dim, n_cell, n_el_facets = self.get_region_info(region)
cmesh = region.domain.mesh.cmesh
if dim == 1:
vols = nm.ones((cmesh.num[0], 1))
else:
vols = cmesh.get_volumes(dim - 1)[:, None]
vols_out = nm.zeros((n_cell, n_el_facets, 1))
c2f = cmesh.get_conn(dim, dim - 1)
for ic, o1 in enumerate(c2f.offsets[:-1]):
o2 = c2f.offsets[ic + 1]
for ifal, ifa in enumerate(c2f.indices[o1:o2]):
vols_out[ic, ifal] = vols[ifa]
self.facet_vols_cache[region.name] = vols_out
return vols_out
def get_data_shape(self, integral, integration='volume', region_name=None):
"""Returns data shape
(n_nod, n_qp, self.gel.dim, self.n_el_nod)
Parameters
----------
integral : integral used
integration :
'volume' is only supported value (Default value = 'volume')
region_name : not used
(Default value = None)
Returns
-------
data_shape : tuple
"""
if integration in ('volume',):
# from FEField.get_data_shape()
_, weights = integral.get_qp(self.gel.name)
n_qp = weights.shape[0]
data_shape = (self.n_cell, n_qp, self.gel.dim, self.n_el_nod)
# econn.shape[1] == n_el_nod i.e. number nod in element
else:
raise NotImplementedError('unsupported integration! (%s)'
% integration)
return data_shape
def get_econn(self, conn_type, region, is_trace=False, integration=None):
"""Getter for econn
Parameters
----------
conn_type : string or Struct
'volume' is only supported
region : sfepy.discrete.common.region.Region
is_trace : ignored
(Default value = False)
integration : ignored
(Default value = None)
Returns
-------
econn : ndarray
connectivity information
"""
ct = conn_type.type if isinstance(conn_type, Struct) else conn_type
if ct == 'volume':
if region.name == self.region.name:
conn = self.econn
else:
raise ValueError("Bad region for the field")
else:
raise ValueError('unknown connectivity type! (%s)' % ct)
return conn
def setup_extra_data(self, geometry, info, is_trace):
"""This is called in create_adof_conns(conn_info, var_indx=None,
active_only=True, verbose=True)
for each variable but has no effect.
Parameters
----------
geometry :
ignored
info :
set to self.info
is_trace :
set to self.trace
"""
# placeholder, what is this used for?
# dct = info.dc_type.type
self.info = info
self.is_trace = is_trace
def get_dofs_in_region(self, region, merge=True):
"""Return indices of DOFs that belong to the given region.
Not Used in BC treatment
Parameters
----------
region : sfepy.discrete.common.region.Region
merge : bool
merge dof tuple into one numpy array, default True
Returns
-------
dofs : ndarray
"""
dofs = []
if region.has_cells(): # main region or its part
els = nm.ravel(self.bubble_remap[region.cells])
eldofs = self.bubble_dofs[els[els >= 0]]
dofs.append(eldofs)
else:
# return indices of cells adjacent to boundary facets
dim = self.dim
cmesh = region.domain.mesh.cmesh
bc_cells = cmesh.get_incident(dim, region.facets, dim - 1)
bc_dofs = self.bubble_dofs[bc_cells]
dofs.append(bc_dofs)
if merge:
dofs = nm.concatenate(dofs)
return dofs
def get_bc_facet_idx(self, region):
"""Caches results in self.boundary_facet_local_idx
Parameters
----------
region : sfepy.discrete.common.region.Region
surface region defining BCs
Returns
-------
bc2bfi : ndarray
index of cells on boundary along with corresponding facets
"""
if region.name in self.boundary_facet_local_idx:
return self.boundary_facet_local_idx[region.name]
bc2bfi = region.get_facet_indices()
self.boundary_facet_local_idx[region.name] = bc2bfi
return bc2bfi
def create_mapping(self, region, integral, integration,
return_mapping=True):
"""Creates and returns mapping
Parameters
----------
region : sfepy.discrete.common.region.Region
integral : Integral
integration : str
'volume' is only accepted option
return_mapping : default True
(Default value = True)
Returns
-------
mapping : VolumeMapping
"""
domain = self.domain
coors = domain.get_mesh_coors(actual=True)
dconn = domain.get_conn()
# from FEField
if integration == 'volume':
qp = self.get_qp('v', integral)
# qp = self.integral.get_qp(self.gel.name)
iels = region.get_cells()
geo_ps = self.gel.poly_space
ps = self.poly_space
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
ori=self.ori,
transform=self.basis_transform)
out = vg
else:
raise ValueError('unsupported integration geometry type: %s'
% integration)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def set_dofs(self, fun=0.0, region=None, dpn=None, warn=None):
"""Compute projection of fun into the basis, alternatively set DOFs
directly to provided value or values either in main volume region
or in boundary region.
Parameters
----------
fun : callable, scalar or array corresponding to dofs
(Default value = 0.0)
region : sfepy.discrete.common.region.Region
region to set DOFs on (Default value = None)
dpn : number of dofs per element
(Default value = None)
warn :
(Default value = None)
Returns
-------
nods : ndarray
vals : ndarray
"""
if region is None:
region = self.region
return self.set_cell_dofs(fun, region, dpn, warn)
elif region.has_cells():
return self.set_cell_dofs(fun, region, dpn, warn)
elif region.kind_tdim == self.dim - 1:
nods, vals = self.set_facet_dofs(fun, region, dpn, warn)
return nods, vals
def set_cell_dofs(self, fun=0.0, region=None, dpn=None, warn=None):
"""
Compute projection of fun onto the basis, in main region, alternatively
set DOFs directly to provided value or values
Parameters
----------
fun : callable, scallar or array corresponding to dofs
(Default value = 0.0)
region : sfepy.discrete.common.region.Region
region to set DOFs on (Default value = None)
dpn : number of dofs per element
(Default value = None)
warn : not used
(Default value = None)
Returns
-------
nods : ndarray
vals : ndarray
"""
aux = self.get_dofs_in_region(region)
nods = nm.unique(nm.hstack(aux))
if nm.isscalar(fun):
vals = nm.zeros(aux.shape)
vals[:, 0] = fun
vals = nm.hstack(vals)
elif isinstance(fun, nm.ndarray):
# useful for testing, allows to pass complete array of dofs as IC
if nm.shape(fun) == nm.shape(nods):
vals = fun
elif callable(fun):
qp, weights = self.integral.get_qp(self.gel.name)
coors = self.mapping.get_physical_qps(qp)
base_vals_qp = self.poly_space.eval_base(qp)[:, 0, :]
# this drops redundant axis that is returned by eval_base due to
# consistency with derivatives
# left hand, so far only orthogonal basis
# for legendre base this can be calculated exactly
# in 1D it is: 1 / (2 * nm.arange(self.n_el_nod) + 1)
lhs_diag = nm.einsum("q,q...->...", weights, base_vals_qp ** 2)
rhs_vec = nm.einsum("q,q...,iq...->i...",
weights, base_vals_qp, fun(coors))
vals = (rhs_vec / lhs_diag)
# plot for 1D
# from utils.visualizer import plot1D_legendre_dofs, reconstruct
# _legendre_dofs
# import matplotlib.pyplot as plt
# plot1D_legendre_dofs(self.domain.mesh.coors, (vals,), fun)
# ww, xx = reconstruct_legendre_dofs(self.domain.mesh.coors, 1,
# vals.T[..., None, None])
# plt.plot(xx, ww[:, 0], label="reconstructed dofs")
# plt.show()
return nods, vals
def set_facet_dofs(self, fun, region, dpn, warn):
"""Compute projection of fun onto the basis on facets, alternatively
set DOFs directly to provided value or values
Parameters
----------
fun : callable, scalar or array corresponding to dofs
region : sfepy.discrete.common.region.Region
region to set DOFs on
dpn : int
number of dofs per element
warn :
not used
Returns
-------
nods : ndarray
vals : ndarray
"""
raise NotImplementedError(
"Setting facet DOFs is not supported with DGField, " +
"use values at qp directly. " +
"This is usually result of using ebc instead of dgebc")
aux = self.get_dofs_in_region(region)
nods = nm.unique(nm.hstack(aux))
if nm.isscalar(fun):
vals = nm.zeros(aux.shape)
vals[:, 0] = fun
vals = nm.hstack(vals)
elif isinstance(fun, nm.ndarray):
assert_(len(fun) == dpn)
vals = nm.zeros(aux.shape)
vals[:, 0] = nm.repeat(fun, vals.shape[0])
elif callable(fun):
vals = nm.zeros(aux.shape)
# set zero DOF to value fun, set other DOFs to zero
# get facets QPs
qp, weights = self.get_facet_qp()
weights = weights[0, :, 0]
qp = qp[:, 0, :, :]
# get facets weights ?
# get coors
bc2bfi = self.get_bc_facet_idx(region)
coors = self.mapping.get_physical_qps(qp)
# get_physical_qps returns data in strange format, swapping
# some axis and flipping qps order
bcoors = coors[bc2bfi[:, 1], ::-1, bc2bfi[:, 0], :]
# get facet basis vals
base_vals_qp = self.poly_space.eval_base(qp)[:, 0, 0, :]
# solve for boundary cell DOFs
bc_val = fun(bcoors)
# this returns singular matrix - projection on the boundary should
# be into facet dim space
#lhs = nm.einsum("q,qd,qc->dc", weights, base_vals_qp, base_vals_qp)
# inv_lhs = nm.linalg.inv(lhs)
# rhs_vec = nm.einsum("q,q...,iq...->i...",
# weights, base_vals_qp, bc_val)
return nods, vals
def get_bc_facet_values(self, fun, region, ret_coors=False, diff=0):
"""Returns values of fun in facet QPs of the region
Parameters
----------
diff: derivative 0 or 1 supported
fun: Function value or values to set qps values to
region : sfepy.discrete.common.region.Region
boundary region
ret_coors: default False,
Return physical coors of qps in shape (n_cell, n_qp, dim).
Returns
-------
vals : ndarray
In shape (n_cell,) + (self.dim,) * diff + (n_qp,)
"""
if region.has_cells():
raise NotImplementedError(
"Region {} has cells and can't be used as boundary region".
format(region))
# get facets QPs
qp, weights = self.get_facet_qp()
weights = weights[0, :, 0]
qp = qp[:, 0, :, :]
n_qp = qp.shape[0]
# get facets weights ?
# get physical coors
bc2bfi = self.get_bc_facet_idx(region)
n_cell = bc2bfi.shape[0]
coors = self.mapping.get_physical_qps(qp)
# get_physical_qps returns data in strange format,
# swapping some axis and flipping qps order
# to get coors in shape (n_facet, n_qp, n_cell, dim)
if len(coors.shape) == 3:
coors = coors[:, None, :, :] # add axis for qps when it is missing
coors = coors.swapaxes(0, 2)
bcoors = coors[bc2bfi[:, 1], ::-1, bc2bfi[:, 0], :]
diff_shape = (self.dim,) * diff
output_shape = (n_cell,) + diff_shape + (n_qp,)
vals = nm.zeros(output_shape)
# we do not need last axis of coors, values are scalars
if nm.isscalar(fun):
if sum(diff_shape) > 1:
output(("Warning: Setting gradient of shape {} "
"in region {} with scalar value {}")
.format(diff_shape, region.name, fun))
vals[:] = fun
elif isinstance(fun, nm.ndarray):
try:
vals[:] = fun[:, None]
except ValueError:
raise ValueError(("Provided values of shape {} could not" +
" be used to set BC qps of shape {} in " +
"region {}")
.format(fun.shape, vals.shape, region.name))
elif callable(fun):
# get boundary values
vals[:] = fun(bcoors)
if ret_coors:
return bcoors, vals
return vals
def get_nodal_values(self, dofs, region, ref_nodes=None):
"""Computes nodal representation of the DOFs
Parameters
---------
dofs : array_like
dofs to transform to nodes
region : ignored
ref_nodes:
reference node to use instead of default qps
Parameters
----------
dofs : array_like
region : Region
ref_nodes : array_like
(Default value = None)
Returns
-------
nodes : ndarray
nodal_vals : ndarray
"""
if ref_nodes is None:
# poly_space could provide special nodes
ref_nodes = self.get_qp('v', self.integral).vals
base_vals_node = self.poly_space.eval_base(ref_nodes)[:, 0, :]
dofs = self.unravel_sol(dofs[:, 0])
nodal_vals = nm.sum(dofs * base_vals_node.T, axis=1)
nodes = self.mapping.get_physical_qps(ref_nodes)
# import matplotlib.pyplot as plt
# plt.plot(nodes[:, 0], nodal_vals)
# plt.show()
return nodes, nodal_vals
def create_output(self, dofs, var_name, dof_names=None,
key=None, extend=True, fill_value=None,
linearization=None):
"""Converts the DOFs corresponding to the field to a dictionary of
output data usable by Mesh.write().
For 1D puts DOFs into vairables u_modal{0} ... u_modal{n}, where
n = approx_order and marks them for writing as cell data.
For 2+D puts dofs into name_cell_nodes and creates sturct with:
mode = "cell_nodes", data and iterpolation scheme.
Also get node values and adds them to dictionary as cell_nodes
Parameters
----------
dofs : ndarray, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
var_name : str
The variable name corresponding to `dofs`.
dof_names : tuple of str
The names of DOF components. (Default value = None)
key : str, optional
The key to be used in the output dictionary instead of the
variable name. (Default value = None)
extend : bool, not used
Extend the DOF values to cover the whole domain.
(Default value = True)
fill_value : float or complex, not used
The value used to fill the missing DOF values if `extend` is True.
(Default value = None)
linearization : Struct or None, not used
The linearization configuration for higher order approximations.
(Default value = None)
Returns
-------
out : dict
"""
out = {}
udofs = self.unravel_sol(dofs)
name = var_name if key is None else key
if self.dim == 1:
for i in range(self.n_el_nod):
out[name + "_modal{}".format(i)] = \
| Struct(mode="cell", data=udofs[:, i, None, None]) | sfepy.base.base.Struct |
from __future__ import absolute_import
input_name = '../examples/multi_physics/piezo_elasticity.py'
output_name = 'test_piezo_elasticity.vtk'
from tests_basic import TestInput
class Test( TestInput ):
def from_conf( conf, options ):
return TestInput.from_conf( conf, options, cls = Test )
from_conf = staticmethod( from_conf )
def test_ebc( self ):
import numpy as nm
from sfepy.discrete import Problem
pb = | Problem.from_conf(self.test_conf) | sfepy.discrete.Problem.from_conf |
"""
Finite element reference mappings.
"""
import numpy as nm
from sfepy import Config
from sfepy.base.base import get_default, output
from sfepy.base.mem_usage import raise_if_too_large
from sfepy.discrete.common.mappings import Mapping
from sfepy.discrete.common.extmods.mappings import CMapping
from sfepy.discrete import PolySpace
class FEMapping(Mapping):
"""
Base class for finite element mappings.
"""
def __init__(self, coors, conn, poly_space=None, gel=None, order=1):
self.coors = coors
self.conn = conn
try:
nm.take(self.coors, self.conn)
except IndexError:
output('coordinates shape: %s' % list(coors.shape))
output('connectivity: min: %d, max: %d' % (conn.min(), conn.max()))
msg = 'incompatible connectivity and coordinates (see above)'
raise IndexError(msg)
self.n_el, self.n_ep = conn.shape
self.dim = self.coors.shape[1]
if poly_space is None:
poly_space = PolySpace.any_from_args(None, gel, order,
base='lagrange',
force_bubble=False)
self.poly_space = poly_space
self.indices = slice(None)
def get_geometry(self):
"""
Return reference element geometry as a GeometryElement instance.
"""
return self.poly_space.geometry
def get_base(self, coors, diff=False):
"""
Get base functions or their gradient evaluated in given
coordinates.
"""
bf = self.poly_space.eval_base(coors, diff=diff)
return bf
def get_physical_qps(self, qp_coors):
"""
Get physical quadrature points corresponding to given reference
element quadrature points.
Returns
-------
qps : array
The physical quadrature points ordered element by element,
i.e. with shape (n_el, n_qp, dim).
"""
bf = self.get_base(qp_coors)
qps = nm.dot(nm.atleast_2d(bf.squeeze()), self.coors[self.conn])
# Reorder so that qps are really element by element.
qps = nm.ascontiguousarray(nm.swapaxes(qps, 0, 1))
return qps
class VolumeMapping(FEMapping):
"""
Mapping from reference domain to physical domain of the same space
dimension.
"""
def get_mapping(self, qp_coors, weights, poly_space=None, ori=None,
transform=None):
"""
Get the mapping for given quadrature points, weights, and
polynomial space.
Returns
-------
cmap : CMapping instance
The volume mapping.
"""
poly_space = | get_default(poly_space, self.poly_space) | sfepy.base.base.get_default |
"""
Finite element reference mappings.
"""
import numpy as nm
from sfepy import Config
from sfepy.base.base import get_default, output
from sfepy.base.mem_usage import raise_if_too_large
from sfepy.discrete.common.mappings import Mapping
from sfepy.discrete.common.extmods.mappings import CMapping
from sfepy.discrete import PolySpace
class FEMapping(Mapping):
"""
Base class for finite element mappings.
"""
def __init__(self, coors, conn, poly_space=None, gel=None, order=1):
self.coors = coors
self.conn = conn
try:
nm.take(self.coors, self.conn)
except IndexError:
output('coordinates shape: %s' % list(coors.shape))
output('connectivity: min: %d, max: %d' % (conn.min(), conn.max()))
msg = 'incompatible connectivity and coordinates (see above)'
raise IndexError(msg)
self.n_el, self.n_ep = conn.shape
self.dim = self.coors.shape[1]
if poly_space is None:
poly_space = PolySpace.any_from_args(None, gel, order,
base='lagrange',
force_bubble=False)
self.poly_space = poly_space
self.indices = slice(None)
def get_geometry(self):
"""
Return reference element geometry as a GeometryElement instance.
"""
return self.poly_space.geometry
def get_base(self, coors, diff=False):
"""
Get base functions or their gradient evaluated in given
coordinates.
"""
bf = self.poly_space.eval_base(coors, diff=diff)
return bf
def get_physical_qps(self, qp_coors):
"""
Get physical quadrature points corresponding to given reference
element quadrature points.
Returns
-------
qps : array
The physical quadrature points ordered element by element,
i.e. with shape (n_el, n_qp, dim).
"""
bf = self.get_base(qp_coors)
qps = nm.dot(nm.atleast_2d(bf.squeeze()), self.coors[self.conn])
# Reorder so that qps are really element by element.
qps = nm.ascontiguousarray(nm.swapaxes(qps, 0, 1))
return qps
class VolumeMapping(FEMapping):
"""
Mapping from reference domain to physical domain of the same space
dimension.
"""
def get_mapping(self, qp_coors, weights, poly_space=None, ori=None,
transform=None):
"""
Get the mapping for given quadrature points, weights, and
polynomial space.
Returns
-------
cmap : CMapping instance
The volume mapping.
"""
poly_space = get_default(poly_space, self.poly_space)
bf_g = self.get_base(qp_coors, diff=True)
ebf_g = poly_space.eval_base(qp_coors, diff=True, ori=ori,
force_axis=True, transform=transform)
size = ebf_g.nbytes * self.n_el
site_config = | Config() | sfepy.Config |
"""
Finite element reference mappings.
"""
import numpy as nm
from sfepy import Config
from sfepy.base.base import get_default, output
from sfepy.base.mem_usage import raise_if_too_large
from sfepy.discrete.common.mappings import Mapping
from sfepy.discrete.common.extmods.mappings import CMapping
from sfepy.discrete import PolySpace
class FEMapping(Mapping):
"""
Base class for finite element mappings.
"""
def __init__(self, coors, conn, poly_space=None, gel=None, order=1):
self.coors = coors
self.conn = conn
try:
nm.take(self.coors, self.conn)
except IndexError:
output('coordinates shape: %s' % list(coors.shape))
output('connectivity: min: %d, max: %d' % (conn.min(), conn.max()))
msg = 'incompatible connectivity and coordinates (see above)'
raise IndexError(msg)
self.n_el, self.n_ep = conn.shape
self.dim = self.coors.shape[1]
if poly_space is None:
poly_space = PolySpace.any_from_args(None, gel, order,
base='lagrange',
force_bubble=False)
self.poly_space = poly_space
self.indices = slice(None)
def get_geometry(self):
"""
Return reference element geometry as a GeometryElement instance.
"""
return self.poly_space.geometry
def get_base(self, coors, diff=False):
"""
Get base functions or their gradient evaluated in given
coordinates.
"""
bf = self.poly_space.eval_base(coors, diff=diff)
return bf
def get_physical_qps(self, qp_coors):
"""
Get physical quadrature points corresponding to given reference
element quadrature points.
Returns
-------
qps : array
The physical quadrature points ordered element by element,
i.e. with shape (n_el, n_qp, dim).
"""
bf = self.get_base(qp_coors)
qps = nm.dot(nm.atleast_2d(bf.squeeze()), self.coors[self.conn])
# Reorder so that qps are really element by element.
qps = nm.ascontiguousarray(nm.swapaxes(qps, 0, 1))
return qps
class VolumeMapping(FEMapping):
"""
Mapping from reference domain to physical domain of the same space
dimension.
"""
def get_mapping(self, qp_coors, weights, poly_space=None, ori=None,
transform=None):
"""
Get the mapping for given quadrature points, weights, and
polynomial space.
Returns
-------
cmap : CMapping instance
The volume mapping.
"""
poly_space = get_default(poly_space, self.poly_space)
bf_g = self.get_base(qp_coors, diff=True)
ebf_g = poly_space.eval_base(qp_coors, diff=True, ori=ori,
force_axis=True, transform=transform)
size = ebf_g.nbytes * self.n_el
site_config = Config()
raise_if_too_large(size, site_config.refmap_memory_factor())
flag = (ori is not None) or (ebf_g.shape[0] > 1)
cmap = CMapping(self.n_el, qp_coors.shape[0], self.dim,
poly_space.n_nod, mode='volume', flag=flag)
cmap.describe(self.coors, self.conn, bf_g, ebf_g, weights)
return cmap
class SurfaceMapping(FEMapping):
"""
Mapping from reference domain to physical domain of the space
dimension higher by one.
"""
def set_basis_indices(self, indices):
"""
Set indices to cell-based basis that give the facet-based basis.
"""
self.indices = indices
def get_base(self, coors, diff=False):
"""
Get base functions or their gradient evaluated in given
coordinates.
"""
bf = self.poly_space.eval_base(coors, diff=diff)
ii = max(self.dim - 1, 1)
return nm.ascontiguousarray(bf[..., :ii:, self.indices])
def get_mapping(self, qp_coors, weights, poly_space=None, mode='surface'):
"""
Get the mapping for given quadrature points, weights, and
polynomial space.
Returns
-------
cmap : CMapping instance
The surface mapping.
"""
poly_space = | get_default(poly_space, self.poly_space) | sfepy.base.base.get_default |
r"""
Incompressible Stokes flow with Navier (slip) boundary conditions, flow driven
by a moving wall and a small diffusion for stabilization.
This example demonstrates the use of `no-penetration` boundary conditions as
well as `edge direction` boundary conditions together with Navier or slip
boundary conditions.
Find :math:`\ul{u}`, :math:`p` such that:
.. math::
\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u}
- \int_{\Omega} p\ \nabla \cdot \ul{v}
+ \int_{\Gamma_1} \beta \ul{v} \cdot (\ul{u} - \ul{u}_d)
+ \int_{\Gamma_2} \beta \ul{v} \cdot \ul{u}
= 0
\;, \quad \forall \ul{v} \;,
\int_{\Omega} \mu \nabla q \cdot \nabla p
+ \int_{\Omega} q\ \nabla \cdot \ul{u}
= 0
\;, \quad \forall q \;,
where :math:`\nu` is the fluid viscosity, :math:`\beta` is the slip
coefficient, :math:`\mu` is the (small) numerical diffusion coefficient,
:math:`\Gamma_1` is the top wall that moves with the given driving velocity
:math:`\ul{u}_d` and :math:`\Gamma_2` are the remaining walls. The Navier
conditions are in effect on both :math:`\Gamma_1`, :math:`\Gamma_2` and are
expressed by the corresponding integrals in the equations above.
The `no-penetration` boundary conditions are applied on :math:`\Gamma_1`,
:math:`\Gamma_2`, except the vertices of the block edges, where the `edge
direction` boundary conditions are applied. Optionally, Dirichlet boundary
conditions can be applied on the inlet, see the code below.
The mesh is created by ``gen_block_mesh()`` function - try different mesh
dimensions and resolutions below. For large meshes use the ``'ls_i'`` linear
solver - PETSc + petsc4py is needed in that case.
"""
import numpy as nm
from sfepy.discrete.fem.meshio import UserMeshIO
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.homogenization.utils import define_box_regions
# Mesh dimensions.
dims = nm.array([3, 1, 0.5])
# Mesh resolution: increase to improve accuracy.
shape = [11, 15, 15]
def mesh_hook(mesh, mode):
"""
Generate the block mesh.
"""
if mode == 'read':
mesh = gen_block_mesh(dims, shape, [0, 0, 0], name='user_block',
verbose=False)
return mesh
elif mode == 'write':
pass
filename_mesh = | UserMeshIO(mesh_hook) | sfepy.discrete.fem.meshio.UserMeshIO |
r"""
Incompressible Stokes flow with Navier (slip) boundary conditions, flow driven
by a moving wall and a small diffusion for stabilization.
This example demonstrates the use of `no-penetration` boundary conditions as
well as `edge direction` boundary conditions together with Navier or slip
boundary conditions.
Find :math:`\ul{u}`, :math:`p` such that:
.. math::
\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u}
- \int_{\Omega} p\ \nabla \cdot \ul{v}
+ \int_{\Gamma_1} \beta \ul{v} \cdot (\ul{u} - \ul{u}_d)
+ \int_{\Gamma_2} \beta \ul{v} \cdot \ul{u}
= 0
\;, \quad \forall \ul{v} \;,
\int_{\Omega} \mu \nabla q \cdot \nabla p
+ \int_{\Omega} q\ \nabla \cdot \ul{u}
= 0
\;, \quad \forall q \;,
where :math:`\nu` is the fluid viscosity, :math:`\beta` is the slip
coefficient, :math:`\mu` is the (small) numerical diffusion coefficient,
:math:`\Gamma_1` is the top wall that moves with the given driving velocity
:math:`\ul{u}_d` and :math:`\Gamma_2` are the remaining walls. The Navier
conditions are in effect on both :math:`\Gamma_1`, :math:`\Gamma_2` and are
expressed by the corresponding integrals in the equations above.
The `no-penetration` boundary conditions are applied on :math:`\Gamma_1`,
:math:`\Gamma_2`, except the vertices of the block edges, where the `edge
direction` boundary conditions are applied. Optionally, Dirichlet boundary
conditions can be applied on the inlet, see the code below.
The mesh is created by ``gen_block_mesh()`` function - try different mesh
dimensions and resolutions below. For large meshes use the ``'ls_i'`` linear
solver - PETSc + petsc4py is needed in that case.
"""
import numpy as nm
from sfepy.discrete.fem.meshio import UserMeshIO
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.homogenization.utils import define_box_regions
# Mesh dimensions.
dims = nm.array([3, 1, 0.5])
# Mesh resolution: increase to improve accuracy.
shape = [11, 15, 15]
def mesh_hook(mesh, mode):
"""
Generate the block mesh.
"""
if mode == 'read':
mesh = gen_block_mesh(dims, shape, [0, 0, 0], name='user_block',
verbose=False)
return mesh
elif mode == 'write':
pass
filename_mesh = UserMeshIO(mesh_hook)
regions = | define_box_regions(3, 0.5 * dims) | sfepy.homogenization.utils.define_box_regions |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = | get_default(conf, self.conf) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = | get_default(mtx_m, self.mtx_m) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = | get_default(mtx_d, self.mtx_d) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = | get_default(mtx_k, self.mtx_k) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = | get_default(n_eigs, self.n_eigs) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = | get_default(eigenvectors, self.eigenvectors) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = | get_default(status, self.status) | sfepy.base.base.get_default |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = | max_diff_csr(mtx_m, mtx_m.T) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = | max_diff_csr(mtx_d, mtx_d.T) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = | max_diff_csr(mtx_k, mtx_k.T) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = | max_diff_csr(mtx_m, mtx_m.H) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = | max_diff_csr(mtx_d, mtx_d.H) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = | max_diff_csr(mtx_k, mtx_k.H) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None],
[None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l],
[mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = | max_diff_csr(mtx_a, mtx_a.T) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None],
[None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l],
[mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = | max_diff_csr(mtx_a, mtx_a.H) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None],
[None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l],
[mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = max_diff_csr(mtx_a, mtx_a.H)
ssym['|B - B^T|'] = | max_diff_csr(mtx_b, mtx_b.T) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None],
[None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l],
[mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = max_diff_csr(mtx_a, mtx_a.H)
ssym['|B - B^T|'] = max_diff_csr(mtx_b, mtx_b.T)
ssym['|B - B^H|'] = | max_diff_csr(mtx_b, mtx_b.H) | sfepy.linalg.utils.max_diff_csr |
"""
Quadratic eigenvalue problem solvers.
"""
from __future__ import absolute_import
import time
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default
from sfepy.linalg.utils import max_diff_csr
from sfepy.solvers.solvers import QuadraticEVPSolver
def standard_call(call):
"""
Decorator handling argument preparation and timing for quadratic
eigensolvers.
"""
def _standard_call(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx_m = get_default(mtx_m, self.mtx_m)
mtx_d = get_default(mtx_d, self.mtx_d)
mtx_k = get_default(mtx_k, self.mtx_k)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_m, mtx_d, mtx_k,
n_eigs, eigenvectors, status, conf,
**kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
class LQuadraticEVPSolver(QuadraticEVPSolver):
"""
Quadratic eigenvalue problem solver based on the problem linearization.
(w^2 M + w D + K) x = 0.
"""
name = 'eig.qevp'
_parameters = [
('method', "{'companion', 'cholesky'}", 'companion', False,
'The linearization method.'),
('solver', 'dict', {'kind': 'eig.scipy', 'method': 'eig'}, False,
"""The configuration of an eigenvalue solver for
the linearized problem (A - w B) x = 0."""),
('mode', "{'normal', 'inverted'}", 'normal', False,
'Solve either A - w B (normal), or B - 1/w A (inverted).'),
('debug', 'bool', False, False,
'If True, print debugging information.'),
]
@standard_call
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = | max_diff_csr(mtx_m, mtx_l * mtx_l.T) | sfepy.linalg.utils.max_diff_csr |
from sfepy.terms.terms import *
from sfepy.linalg import dot_sequences
class NonPenetrationTerm(Term):
r"""
:Description:
Non-penetration condition in the weak sense.
:Definition:
.. math::
\int_{\Gamma} \lambda \ul{n} \cdot \ul{v} \mbox{ , }
\int_{\Gamma} \hat\lambda \ul{n} \cdot \ul{u}
:Arguments 1:
virtual : :math:`\ul{v}`,
state : :math:`\lambda`
:Arguments 2:
state : :math:`\ul{u}`,
virtual : :math:`\hat\lambda`
"""
name = 'dw_non_penetration'
arg_types = (('virtual', 'state'),
('state', 'virtual'))
modes = ('grad', 'div')
integration = 'surface'
use_caches = {'state_in_surface_qp' : [['state']]}
def __call__(self, diff_var=None, **kwargs):
if self.mode == 'grad':
virtual, state = self.get_args(**kwargs)
ap, sg = self.get_approximation(virtual)
cache = self.get_cache('state_in_surface_qp', 0)
else:
state, virtual = self.get_args(**kwargs)
ap, sg = self.get_approximation(state)
cache = self.get_cache('state_in_surface_qp', 0)
n_fa, n_qp, dim, n_fp = ap.get_s_data_shape(self.integral,
self.region.name)
rdim, cdim = virtual.n_components, state.n_components
if diff_var is None:
shape = (n_fa, 1, rdim * n_fp, 1)
elif diff_var == self.get_arg_name('state'):
shape = (n_fa, 1, rdim * n_fp, cdim * n_fp)
else:
raise StopIteration
sd = ap.surface_data[self.region.name]
# ap corresponds to \ul{u} field.
bf = ap.get_base(sd.face_type, 0, integral=self.integral)
ebf = nm.zeros((bf.shape[0], dim, n_fp * dim),
dtype=nm.float64)
for ir in xrange(dim):
ebf[:, ir, ir*n_fp:(ir+1)*n_fp] = bf[:,0,:]
normals = sg.variable(0)
out = nm.zeros(shape, dtype=nm.float64)
lchunk = nm.arange(n_fa, dtype=nm.int32)
if diff_var is None:
vec_qp = cache('state', self, 0,
state=state, get_vector=self.get_vector)
if self.mode == 'grad':
ebf_t = nm.tile(ebf.transpose((0, 2, 1)), (n_fa, 1, 1, 1))
nl = normals * vec_qp
eftnl = dot_sequences(ebf_t, nl, use_rows=True)
sg.integrate_chunk(out, eftnl, lchunk, 1)
else:
bf_t = nm.tile(bf.transpose((0, 2, 1)), (n_fa, 1, 1, 1))
ntu = (normals * vec_qp).sum(axis=-2)[...,None]
ftntu = (bf_t * ntu)
sg.integrate_chunk(out, ftntu, lchunk, 1)
else:
ebf_t = nm.tile(ebf.transpose((0, 2, 1)), (n_fa, 1, 1, 1))
bf_ = nm.tile(bf, (n_fa, 1, 1, 1))
eftn = | dot_sequences(ebf_t, normals, use_rows=True) | sfepy.linalg.dot_sequences |
from sfepy.terms.terms import *
from sfepy.linalg import dot_sequences
class NonPenetrationTerm(Term):
r"""
:Description:
Non-penetration condition in the weak sense.
:Definition:
.. math::
\int_{\Gamma} \lambda \ul{n} \cdot \ul{v} \mbox{ , }
\int_{\Gamma} \hat\lambda \ul{n} \cdot \ul{u}
:Arguments 1:
virtual : :math:`\ul{v}`,
state : :math:`\lambda`
:Arguments 2:
state : :math:`\ul{u}`,
virtual : :math:`\hat\lambda`
"""
name = 'dw_non_penetration'
arg_types = (('virtual', 'state'),
('state', 'virtual'))
modes = ('grad', 'div')
integration = 'surface'
use_caches = {'state_in_surface_qp' : [['state']]}
def __call__(self, diff_var=None, **kwargs):
if self.mode == 'grad':
virtual, state = self.get_args(**kwargs)
ap, sg = self.get_approximation(virtual)
cache = self.get_cache('state_in_surface_qp', 0)
else:
state, virtual = self.get_args(**kwargs)
ap, sg = self.get_approximation(state)
cache = self.get_cache('state_in_surface_qp', 0)
n_fa, n_qp, dim, n_fp = ap.get_s_data_shape(self.integral,
self.region.name)
rdim, cdim = virtual.n_components, state.n_components
if diff_var is None:
shape = (n_fa, 1, rdim * n_fp, 1)
elif diff_var == self.get_arg_name('state'):
shape = (n_fa, 1, rdim * n_fp, cdim * n_fp)
else:
raise StopIteration
sd = ap.surface_data[self.region.name]
# ap corresponds to \ul{u} field.
bf = ap.get_base(sd.face_type, 0, integral=self.integral)
ebf = nm.zeros((bf.shape[0], dim, n_fp * dim),
dtype=nm.float64)
for ir in xrange(dim):
ebf[:, ir, ir*n_fp:(ir+1)*n_fp] = bf[:,0,:]
normals = sg.variable(0)
out = nm.zeros(shape, dtype=nm.float64)
lchunk = nm.arange(n_fa, dtype=nm.int32)
if diff_var is None:
vec_qp = cache('state', self, 0,
state=state, get_vector=self.get_vector)
if self.mode == 'grad':
ebf_t = nm.tile(ebf.transpose((0, 2, 1)), (n_fa, 1, 1, 1))
nl = normals * vec_qp
eftnl = | dot_sequences(ebf_t, nl, use_rows=True) | sfepy.linalg.dot_sequences |
r"""
Diametrically point loaded 2-D disk with postprocessing and probes. See
:ref:`sec-primer`.
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}
\;.
"""
from __future__ import absolute_import
from examples.linear_elasticity.its2D_1 import *
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson
from sfepy.postprocess.probes_vtk import Probe
import os
from six.moves import range
def stress_strain(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
import matplotlib.pyplot as plt
import matplotlib.font_manager as fm
ev = pb.evaluate
strain = ev('ev_cauchy_strain.2.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.2.Omega(Asphalt.D, u)', mode='el_avg')
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
probe = | Probe(out, pb.domain.mesh, probe_view=True) | sfepy.postprocess.probes_vtk.Probe |
r"""
Diametrically point loaded 2-D disk with postprocessing and probes. See
:ref:`sec-primer`.
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}
\;.
"""
from __future__ import absolute_import
from examples.linear_elasticity.its2D_1 import *
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson
from sfepy.postprocess.probes_vtk import Probe
import os
from six.moves import range
def stress_strain(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
import matplotlib.pyplot as plt
import matplotlib.font_manager as fm
ev = pb.evaluate
strain = ev('ev_cauchy_strain.2.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.2.Omega(Asphalt.D, u)', mode='el_avg')
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
probe = Probe(out, pb.domain.mesh, probe_view=True)
ps0 = [[0.0, 0.0, 0.0], [ 0.0, 0.0, 0.0]]
ps1 = [[75.0, 0.0, 0.0], [ 0.0, 75.0, 0.0]]
n_point = 10
labels = ['%s -> %s' % (p0, p1) for p0, p1 in zip(ps0, ps1)]
probes = []
for ip in range(len(ps0)):
p0, p1 = ps0[ip], ps1[ip]
probes.append('line%d' % ip)
probe.add_line_probe('line%d' % ip, p0, p1, n_point)
for ip, label in zip(probes, labels):
fig = plt.figure()
plt.clf()
fig.subplots_adjust(hspace=0.4)
plt.subplot(311)
pars, vals = probe(ip, 'u')
for ic in range(vals.shape[1] - 1):
plt.plot(pars, vals[:,ic], label=r'$u_{%d}$' % (ic + 1),
lw=1, ls='-', marker='+', ms=3)
plt.ylabel('displacements')
plt.xlabel('probe %s' % label, fontsize=8)
plt.legend(loc='best', prop=fm.FontProperties(size=10))
sym_indices = [0, 4, 1]
sym_labels = ['11', '22', '12']
plt.subplot(312)
pars, vals = probe(ip, 'cauchy_strain')
for ii, ic in enumerate(sym_indices):
plt.plot(pars, vals[:,ic], label=r'$e_{%s}$' % sym_labels[ii],
lw=1, ls='-', marker='+', ms=3)
plt.ylabel('Cauchy strain')
plt.xlabel('probe %s' % label, fontsize=8)
plt.legend(loc='best', prop=fm.FontProperties(size=8))
plt.subplot(313)
pars, vals = probe(ip, 'cauchy_stress')
for ii, ic in enumerate(sym_indices):
plt.plot(pars, vals[:,ic], label=r'$\sigma_{%s}$' % sym_labels[ii],
lw=1, ls='-', marker='+', ms=3)
plt.ylabel('Cauchy stress')
plt.xlabel('probe %s' % label, fontsize=8)
plt.legend(loc='best', prop=fm.FontProperties(size=8))
opts = pb.conf.options
filename_results = os.path.join(opts.get('output_dir'),
'its2D_probe_%s.png' % ip)
fig.savefig(filename_results)
return out
materials['Asphalt'][0].update({'D' : | stiffness_from_youngpoisson(2, young, poisson) | sfepy.mechanics.matcoefs.stiffness_from_youngpoisson |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
| output.set_output(quiet=True) | sfepy.base.base.output.set_output |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: | EssentialBC("fix_points_BC", x, cond) | sfepy.discrete.conditions.EssentialBC |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function= | Function("material_func", _material_func_) | sfepy.discrete.Function |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: | Domain("domain", x) | sfepy.discrete.fem.FEDomain |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: | Field.from_args("fu", np.float64, "vector", x, approx_order=2) | sfepy.discrete.fem.Field.from_args |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
# field = Field.from_args('fu', np.float64, 'vector', region_all,
# pylint: disable=no-member
# approx_order=2)
def get_terms(u_field, v_field, calc_stiffness, calc_prestress):
"""Get the terms for the equation
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a function to calculate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
Returns:
a tuple of terms for the equation
"""
return (
Term.new(
"dw_lin_elastic(m.D, v, u)",
| Integral("i", order=4) | sfepy.discrete.Integral |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
# field = Field.from_args('fu', np.float64, 'vector', region_all,
# pylint: disable=no-member
# approx_order=2)
def get_terms(u_field, v_field, calc_stiffness, calc_prestress):
"""Get the terms for the equation
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a function to calculate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
Returns:
a tuple of terms for the equation
"""
return (
Term.new(
"dw_lin_elastic(m.D, v, u)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
u=u_field,
),
Term.new(
"dw_lin_prestress(m.stress, v)",
| Integral("i", order=4) | sfepy.discrete.Integral |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
# field = Field.from_args('fu', np.float64, 'vector', region_all,
# pylint: disable=no-member
# approx_order=2)
def get_terms(u_field, v_field, calc_stiffness, calc_prestress):
"""Get the terms for the equation
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a function to calculate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
Returns:
a tuple of terms for the equation
"""
return (
Term.new(
"dw_lin_elastic(m.D, v, u)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
u=u_field,
),
Term.new(
"dw_lin_prestress(m.stress, v)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
),
)
def get_nls(evaluator):
"""Get the non-linear solver
Args:
evaluator: the problem evaluator
Returns:
the non-linear solver
"""
return Newton(
{},
lin_solver= | ScipyDirect({}) | sfepy.solvers.ls.ScipyDirect |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
| FieldVariable("u", "unknown", x) | sfepy.discrete.FieldVariable |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
| FieldVariable("v", "test", x, primary_var_name="u") | sfepy.discrete.FieldVariable |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
# field = Field.from_args('fu', np.float64, 'vector', region_all,
# pylint: disable=no-member
# approx_order=2)
def get_terms(u_field, v_field, calc_stiffness, calc_prestress):
"""Get the terms for the equation
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a function to calculate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
Returns:
a tuple of terms for the equation
"""
return (
Term.new(
"dw_lin_elastic(m.D, v, u)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
u=u_field,
),
Term.new(
"dw_lin_prestress(m.stress, v)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
),
)
def get_nls(evaluator):
"""Get the non-linear solver
Args:
evaluator: the problem evaluator
Returns:
the non-linear solver
"""
return Newton(
{},
lin_solver=ScipyDirect({}),
fun=evaluator.eval_residual,
fun_grad=evaluator.eval_tangent_matrix,
)
def get_problem(u_field, v_field, calc_stiffness, calc_prestress, delta_x):
"""Get the problem
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a functioin to calcuate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
delta_x: the mesh spacing
Returns:
the Sfepy problem
"""
return pipe(
get_terms(u_field, v_field, calc_stiffness, calc_prestress),
lambda x: Equation("balance_of_forces", | Terms([x[0], x[1]]) | sfepy.terms.Terms |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions= | Functions([x]) | sfepy.discrete.Functions |
"""All Sfepy imports go in this module
"""
import numpy as np
from sfepy.base.goptions import goptions
from sfepy.discrete.fem import Field
from sfepy.discrete.fem import FEDomain as Domain
from sfepy.discrete import (
FieldVariable,
Material,
Integral,
Function,
Equation,
Equations,
Problem,
)
from sfepy.terms import Term, Terms
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.discrete import Functions
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.base.base import output
from toolz.curried import pipe, curry, do
goptions["verbose"] = False
output.set_output(quiet=True)
def check(ids):
"""Check that the fixed displacement nodes have been isolated
Args:
ids: the isolated IDs
Returns the unchanged IDs
>>> check([1, 2, 3, 4])
Traceback (most recent call last):
...
RuntimeError: length of ids is incorrect
"""
if len(ids) != 3:
raise RuntimeError("length of ids is incorrect")
return ids
@curry
def subdomain(i_x, domain_, eps, coords, **_):
"""Find the node IDs that will be fixed
Args:
i_x: the index (either 0 or 1) depends on direction of axes
domain_: the Sfepy domain
eps: a small value
coords: the coordinates of the nodes
Returns:
the isolated node IDs
"""
def i_y():
"""Switch the index from 0 -> 1 or from 1 -> 0
"""
return (i_x + 1) % 2
return pipe(
(coords[:, i_x] > -eps) & (coords[:, i_x] < eps),
lambda x: (coords[:, i_x] < domain_.get_mesh_bounding_box()[0][i_x] + eps) | x,
lambda x: (coords[:, i_x] > domain_.get_mesh_bounding_box()[1][i_x] - eps) | x,
lambda x: (coords[:, i_y()] < eps) & (coords[:, i_y()] > -eps) & x,
lambda x: np.where(x)[0],
check,
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def get_bcs(domain, delta_x):
"""Get the boundary conditions
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
Returns:
the boundary conditions
"""
return Conditions(
[
get_bc(domain, delta_x, 1, {"u.0": 0.0}),
get_bc(domain, delta_x, 0, {"u.1": 0.0}),
]
)
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def get_uv(shape, delta_x):
"""Get the fields for the displacement and test function
Args:
shape: the shape of the domain
delta_x: the mesh spacing
Returns:
tuple of field variables
"""
return pipe(
np.array(shape),
lambda x: gen_block_mesh(
x * delta_x, x + 1, np.zeros_like(shape), verbose=False
),
lambda x: Domain("domain", x),
lambda x: x.create_region("region_all", "all"),
lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
lambda x: (
FieldVariable("u", "unknown", x),
FieldVariable("v", "test", x, primary_var_name="u"),
),
)
# field = Field.from_args('fu', np.float64, 'vector', region_all,
# pylint: disable=no-member
# approx_order=2)
def get_terms(u_field, v_field, calc_stiffness, calc_prestress):
"""Get the terms for the equation
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a function to calculate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
Returns:
a tuple of terms for the equation
"""
return (
Term.new(
"dw_lin_elastic(m.D, v, u)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
u=u_field,
),
Term.new(
"dw_lin_prestress(m.stress, v)",
Integral("i", order=4),
v_field.field.region,
m=get_material(calc_stiffness, calc_prestress),
v=v_field,
),
)
def get_nls(evaluator):
"""Get the non-linear solver
Args:
evaluator: the problem evaluator
Returns:
the non-linear solver
"""
return Newton(
{},
lin_solver=ScipyDirect({}),
fun=evaluator.eval_residual,
fun_grad=evaluator.eval_tangent_matrix,
)
def get_problem(u_field, v_field, calc_stiffness, calc_prestress, delta_x):
"""Get the problem
Args:
u_field: the displacement field
v_field: the test function field
calc_stiffness: a functioin to calcuate the stiffness tensor
calc_prestress: a function to calculate the prestress tensor
delta_x: the mesh spacing
Returns:
the Sfepy problem
"""
return pipe(
get_terms(u_field, v_field, calc_stiffness, calc_prestress),
lambda x: Equation("balance_of_forces", Terms([x[0], x[1]])),
lambda x: Problem("elasticity", equations= | Equations([x]) | sfepy.discrete.Equations |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = | get_default(solver_class, ScipyDirect) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = | get_default(solver_conf, {}) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = | Timer(start=True) | sfepy.base.timing.Timer |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = | get_default(conf, self.conf) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = | get_default(mtx, self.mtx) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = | get_default(status, self.status) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = | get_default(context, self.context) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
| assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0]) | sfepy.base.base.assert_ |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = | Timer(start=True) | sfepy.base.timing.Timer |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = | get_default(conf, self.conf) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = | get_default(mtx, self.mtx) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = | get_default(status, self.status) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = | get_default(context, self.context) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = | get_default(comm, self.comm) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = get_default(comm, self.comm)
mshape = mtx.size if isinstance(mtx, self.petsc.Mat) else mtx.shape
rshape = [rhs.size] if isinstance(rhs, self.petsc.Vec) else rhs.shape
| assert_(mshape[0] == mshape[1] == rshape[0]) | sfepy.base.base.assert_ |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = get_default(comm, self.comm)
mshape = mtx.size if isinstance(mtx, self.petsc.Mat) else mtx.shape
rshape = [rhs.size] if isinstance(rhs, self.petsc.Vec) else rhs.shape
assert_(mshape[0] == mshape[1] == rshape[0])
if x0 is not None:
xshape = [x0.size] if isinstance(x0, self.petsc.Vec) else x0.shape
assert_(xshape[0] == rshape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
comm, context=context, **kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = self.ksp.getIterationNumber()
return result
return _petsc_call
class ScipyDirect(LinearSolver):
"""
Direct sparse solver from SciPy.
"""
name = 'ls.scipy_direct'
_parameters = [
('method', "{'auto', 'umfpack', 'superlu'}", 'auto', False,
'The actual solver to use.'),
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, method=None, **kwargs):
| LinearSolver.__init__(self, conf, solve=None, **kwargs) | sfepy.solvers.solvers.LinearSolver.__init__ |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = get_default(comm, self.comm)
mshape = mtx.size if isinstance(mtx, self.petsc.Mat) else mtx.shape
rshape = [rhs.size] if isinstance(rhs, self.petsc.Vec) else rhs.shape
assert_(mshape[0] == mshape[1] == rshape[0])
if x0 is not None:
xshape = [x0.size] if isinstance(x0, self.petsc.Vec) else x0.shape
assert_(xshape[0] == rshape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
comm, context=context, **kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = self.ksp.getIterationNumber()
return result
return _petsc_call
class ScipyDirect(LinearSolver):
"""
Direct sparse solver from SciPy.
"""
name = 'ls.scipy_direct'
_parameters = [
('method', "{'auto', 'umfpack', 'superlu'}", 'auto', False,
'The actual solver to use.'),
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, method=None, **kwargs):
LinearSolver.__init__(self, conf, solve=None, **kwargs)
um = self.sls = None
if method is None:
method = self.conf.method
aux = try_imports(['import scipy.linsolve as sls',
'import scipy.splinalg.dsolve as sls',
'import scipy.sparse.linalg.dsolve as sls'],
'cannot import scipy sparse direct solvers!')
if 'sls' in aux:
self.sls = aux['sls']
else:
raise ValueError('SuperLU not available!')
if method in ['auto', 'umfpack']:
aux = try_imports([
'import scipy.linsolve.umfpack as um',
'import scipy.splinalg.dsolve.umfpack as um',
'import scipy.sparse.linalg.dsolve.umfpack as um',
'import scikits.umfpack as um'])
is_umfpack = True if 'um' in aux\
and hasattr(aux['um'], 'UMFPACK_OK') else False
if method == 'umfpack' and not is_umfpack:
raise ValueError('UMFPACK not available!')
elif method == 'superlu':
is_umfpack = False
else:
raise ValueError('uknown solution method! (%s)' % method)
if is_umfpack:
self.sls.use_solver(useUmfpack=True,
assumeSortedIndices=True)
else:
self.sls.use_solver(useUmfpack=False)
@standard_call
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, **kwargs):
if conf.use_presolve:
self.presolve(mtx)
if self.solve is not None:
# Matrix is already prefactorized.
return self.solve(rhs)
else:
return self.sls.spsolve(mtx, rhs)
def presolve(self, mtx):
is_new, mtx_digest = _is_new_matrix(mtx, self.mtx_digest)
if is_new:
self.solve = self.sls.factorized(mtx)
self.mtx_digest = mtx_digest
class ScipySuperLU(ScipyDirect):
"""
SuperLU - direct sparse solver from SciPy.
"""
name = 'ls.scipy_superlu'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='superlu', **kwargs)
class ScipyUmfpack(ScipyDirect):
"""
UMFPACK - direct sparse solver from SciPy.
"""
name = 'ls.scipy_umfpack'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='umfpack', **kwargs)
class ScipyIterative(LinearSolver):
"""
Interface to SciPy iterative solvers.
The `eps_r` tolerance is both absolute and relative - the solvers
stop when either the relative or the absolute residual is below it.
"""
name = 'ls.scipy_iterative'
_parameters = [
('method', 'str', 'cg', False,
'The actual solver to use.'),
('setup_precond', 'callable', lambda mtx, context: None, False,
"""User-supplied function for the preconditioner initialization/setup.
It is called as setup_precond(mtx, context), where mtx is the
matrix, context is a user-supplied context, and should return one
of {sparse matrix, dense matrix, LinearOperator}.
"""),
('callback', 'callable', None, False,
"""User-supplied function to call after each iteration. It is called
as callback(xk), where xk is the current solution vector, except
the gmres method, where the argument is the residual.
"""),
('i_max', 'int', 100, False,
'The maximum number of iterations.'),
('eps_a', 'float', 1e-8, False,
'The absolute tolerance for the residual.'),
('eps_r', 'float', 1e-8, False,
'The relative tolerance for the residual.'),
('*', '*', None, False,
'Additional parameters supported by the method.'),
]
# All iterative solvers in scipy.sparse.linalg pass a solution vector into
# a callback except those below, that take a residual vector.
_callbacks_res = ['gmres']
def __init__(self, conf, context=None, **kwargs):
import scipy.sparse.linalg.isolve as la
| LinearSolver.__init__(self, conf, context=context, **kwargs) | sfepy.solvers.solvers.LinearSolver.__init__ |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = get_default(comm, self.comm)
mshape = mtx.size if isinstance(mtx, self.petsc.Mat) else mtx.shape
rshape = [rhs.size] if isinstance(rhs, self.petsc.Vec) else rhs.shape
assert_(mshape[0] == mshape[1] == rshape[0])
if x0 is not None:
xshape = [x0.size] if isinstance(x0, self.petsc.Vec) else x0.shape
assert_(xshape[0] == rshape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
comm, context=context, **kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = self.ksp.getIterationNumber()
return result
return _petsc_call
class ScipyDirect(LinearSolver):
"""
Direct sparse solver from SciPy.
"""
name = 'ls.scipy_direct'
_parameters = [
('method', "{'auto', 'umfpack', 'superlu'}", 'auto', False,
'The actual solver to use.'),
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, method=None, **kwargs):
LinearSolver.__init__(self, conf, solve=None, **kwargs)
um = self.sls = None
if method is None:
method = self.conf.method
aux = try_imports(['import scipy.linsolve as sls',
'import scipy.splinalg.dsolve as sls',
'import scipy.sparse.linalg.dsolve as sls'],
'cannot import scipy sparse direct solvers!')
if 'sls' in aux:
self.sls = aux['sls']
else:
raise ValueError('SuperLU not available!')
if method in ['auto', 'umfpack']:
aux = try_imports([
'import scipy.linsolve.umfpack as um',
'import scipy.splinalg.dsolve.umfpack as um',
'import scipy.sparse.linalg.dsolve.umfpack as um',
'import scikits.umfpack as um'])
is_umfpack = True if 'um' in aux\
and hasattr(aux['um'], 'UMFPACK_OK') else False
if method == 'umfpack' and not is_umfpack:
raise ValueError('UMFPACK not available!')
elif method == 'superlu':
is_umfpack = False
else:
raise ValueError('uknown solution method! (%s)' % method)
if is_umfpack:
self.sls.use_solver(useUmfpack=True,
assumeSortedIndices=True)
else:
self.sls.use_solver(useUmfpack=False)
@standard_call
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, **kwargs):
if conf.use_presolve:
self.presolve(mtx)
if self.solve is not None:
# Matrix is already prefactorized.
return self.solve(rhs)
else:
return self.sls.spsolve(mtx, rhs)
def presolve(self, mtx):
is_new, mtx_digest = _is_new_matrix(mtx, self.mtx_digest)
if is_new:
self.solve = self.sls.factorized(mtx)
self.mtx_digest = mtx_digest
class ScipySuperLU(ScipyDirect):
"""
SuperLU - direct sparse solver from SciPy.
"""
name = 'ls.scipy_superlu'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='superlu', **kwargs)
class ScipyUmfpack(ScipyDirect):
"""
UMFPACK - direct sparse solver from SciPy.
"""
name = 'ls.scipy_umfpack'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='umfpack', **kwargs)
class ScipyIterative(LinearSolver):
"""
Interface to SciPy iterative solvers.
The `eps_r` tolerance is both absolute and relative - the solvers
stop when either the relative or the absolute residual is below it.
"""
name = 'ls.scipy_iterative'
_parameters = [
('method', 'str', 'cg', False,
'The actual solver to use.'),
('setup_precond', 'callable', lambda mtx, context: None, False,
"""User-supplied function for the preconditioner initialization/setup.
It is called as setup_precond(mtx, context), where mtx is the
matrix, context is a user-supplied context, and should return one
of {sparse matrix, dense matrix, LinearOperator}.
"""),
('callback', 'callable', None, False,
"""User-supplied function to call after each iteration. It is called
as callback(xk), where xk is the current solution vector, except
the gmres method, where the argument is the residual.
"""),
('i_max', 'int', 100, False,
'The maximum number of iterations.'),
('eps_a', 'float', 1e-8, False,
'The absolute tolerance for the residual.'),
('eps_r', 'float', 1e-8, False,
'The relative tolerance for the residual.'),
('*', '*', None, False,
'Additional parameters supported by the method.'),
]
# All iterative solvers in scipy.sparse.linalg pass a solution vector into
# a callback except those below, that take a residual vector.
_callbacks_res = ['gmres']
def __init__(self, conf, context=None, **kwargs):
import scipy.sparse.linalg.isolve as la
LinearSolver.__init__(self, conf, context=context, **kwargs)
try:
solver = getattr(la, self.conf.method)
except AttributeError:
output('scipy solver %s does not exist!' % self.conf.method)
output('using cg instead')
solver = la.cg
self.solver = solver
self.converged_reasons = {
0 : 'successful exit',
1 : 'number of iterations',
-1 : 'illegal input or breakdown',
}
@standard_call
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None, **kwargs):
solver_kwargs = self.build_solver_kwargs(conf)
eps_a = | get_default(eps_a, self.conf.eps_a) | sfepy.base.base.get_default |
from __future__ import absolute_import
import hashlib
import numpy as nm
import warnings
import scipy.sparse as sps
import six
from six.moves import range
warnings.simplefilter('ignore', sps.SparseEfficiencyWarning)
from sfepy.base.base import output, get_default, assert_, try_imports
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import LinearSolver
def solve(mtx, rhs, solver_class=None, solver_conf=None):
"""
Solve the linear system with the matrix `mtx` and the right-hand side
`rhs`.
Convenience wrapper around the linear solver classes below.
"""
solver_class = get_default(solver_class, ScipyDirect)
solver_conf = get_default(solver_conf, {})
solver = solver_class(solver_conf, mtx=mtx)
solution = solver(rhs)
return solution
def _get_cs_matrix_hash(mtx, chunk_size=100000):
def _gen_array_chunks(arr):
ii = 0
while len(arr[ii:]):
yield arr[ii:ii+chunk_size].tobytes()
ii += chunk_size
sha1 = hashlib.sha1()
for chunk in _gen_array_chunks(mtx.indptr):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.indices):
sha1.update(chunk)
for chunk in _gen_array_chunks(mtx.data):
sha1.update(chunk)
digest = sha1.hexdigest()
return digest
def _is_new_matrix(mtx, mtx_digest, force_reuse=False):
if not isinstance(mtx, sps.csr_matrix):
return True, mtx_digest
if force_reuse:
return False, mtx_digest
id0, digest0 = mtx_digest
id1 = id(mtx)
digest1 = _get_cs_matrix_hash(mtx)
if (id1 == id0) and (digest1 == digest0):
return False, (id1, digest1)
return True, (id1, digest1)
def standard_call(call):
"""
Decorator handling argument preparation and timing for linear solvers.
"""
def _standard_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None,
**kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
assert_(mtx.shape[0] == mtx.shape[1] == rhs.shape[0])
if x0 is not None:
assert_(x0.shape[0] == rhs.shape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
context=context, **kwargs)
if isinstance(result, tuple):
result, n_iter = result
else:
n_iter = -1 # Number of iterations is undefined/unavailable.
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = n_iter
return result
return _standard_call
def petsc_call(call):
"""
Decorator handling argument preparation and timing for PETSc-based linear
solvers.
"""
def _petsc_call(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, comm=None,
context=None, **kwargs):
timer = Timer(start=True)
conf = get_default(conf, self.conf)
mtx = get_default(mtx, self.mtx)
status = get_default(status, self.status)
context = get_default(context, self.context)
comm = get_default(comm, self.comm)
mshape = mtx.size if isinstance(mtx, self.petsc.Mat) else mtx.shape
rshape = [rhs.size] if isinstance(rhs, self.petsc.Vec) else rhs.shape
assert_(mshape[0] == mshape[1] == rshape[0])
if x0 is not None:
xshape = [x0.size] if isinstance(x0, self.petsc.Vec) else x0.shape
assert_(xshape[0] == rshape[0])
result = call(self, rhs, x0, conf, eps_a, eps_r, i_max, mtx, status,
comm, context=context, **kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
status['n_iter'] = self.ksp.getIterationNumber()
return result
return _petsc_call
class ScipyDirect(LinearSolver):
"""
Direct sparse solver from SciPy.
"""
name = 'ls.scipy_direct'
_parameters = [
('method', "{'auto', 'umfpack', 'superlu'}", 'auto', False,
'The actual solver to use.'),
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, method=None, **kwargs):
LinearSolver.__init__(self, conf, solve=None, **kwargs)
um = self.sls = None
if method is None:
method = self.conf.method
aux = try_imports(['import scipy.linsolve as sls',
'import scipy.splinalg.dsolve as sls',
'import scipy.sparse.linalg.dsolve as sls'],
'cannot import scipy sparse direct solvers!')
if 'sls' in aux:
self.sls = aux['sls']
else:
raise ValueError('SuperLU not available!')
if method in ['auto', 'umfpack']:
aux = try_imports([
'import scipy.linsolve.umfpack as um',
'import scipy.splinalg.dsolve.umfpack as um',
'import scipy.sparse.linalg.dsolve.umfpack as um',
'import scikits.umfpack as um'])
is_umfpack = True if 'um' in aux\
and hasattr(aux['um'], 'UMFPACK_OK') else False
if method == 'umfpack' and not is_umfpack:
raise ValueError('UMFPACK not available!')
elif method == 'superlu':
is_umfpack = False
else:
raise ValueError('uknown solution method! (%s)' % method)
if is_umfpack:
self.sls.use_solver(useUmfpack=True,
assumeSortedIndices=True)
else:
self.sls.use_solver(useUmfpack=False)
@standard_call
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, **kwargs):
if conf.use_presolve:
self.presolve(mtx)
if self.solve is not None:
# Matrix is already prefactorized.
return self.solve(rhs)
else:
return self.sls.spsolve(mtx, rhs)
def presolve(self, mtx):
is_new, mtx_digest = _is_new_matrix(mtx, self.mtx_digest)
if is_new:
self.solve = self.sls.factorized(mtx)
self.mtx_digest = mtx_digest
class ScipySuperLU(ScipyDirect):
"""
SuperLU - direct sparse solver from SciPy.
"""
name = 'ls.scipy_superlu'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='superlu', **kwargs)
class ScipyUmfpack(ScipyDirect):
"""
UMFPACK - direct sparse solver from SciPy.
"""
name = 'ls.scipy_umfpack'
_parameters = [
('use_presolve', 'bool', False, False,
'If True, pre-factorize the matrix.'),
]
def __init__(self, conf, **kwargs):
ScipyDirect.__init__(self, conf, method='umfpack', **kwargs)
class ScipyIterative(LinearSolver):
"""
Interface to SciPy iterative solvers.
The `eps_r` tolerance is both absolute and relative - the solvers
stop when either the relative or the absolute residual is below it.
"""
name = 'ls.scipy_iterative'
_parameters = [
('method', 'str', 'cg', False,
'The actual solver to use.'),
('setup_precond', 'callable', lambda mtx, context: None, False,
"""User-supplied function for the preconditioner initialization/setup.
It is called as setup_precond(mtx, context), where mtx is the
matrix, context is a user-supplied context, and should return one
of {sparse matrix, dense matrix, LinearOperator}.
"""),
('callback', 'callable', None, False,
"""User-supplied function to call after each iteration. It is called
as callback(xk), where xk is the current solution vector, except
the gmres method, where the argument is the residual.
"""),
('i_max', 'int', 100, False,
'The maximum number of iterations.'),
('eps_a', 'float', 1e-8, False,
'The absolute tolerance for the residual.'),
('eps_r', 'float', 1e-8, False,
'The relative tolerance for the residual.'),
('*', '*', None, False,
'Additional parameters supported by the method.'),
]
# All iterative solvers in scipy.sparse.linalg pass a solution vector into
# a callback except those below, that take a residual vector.
_callbacks_res = ['gmres']
def __init__(self, conf, context=None, **kwargs):
import scipy.sparse.linalg.isolve as la
LinearSolver.__init__(self, conf, context=context, **kwargs)
try:
solver = getattr(la, self.conf.method)
except AttributeError:
output('scipy solver %s does not exist!' % self.conf.method)
output('using cg instead')
solver = la.cg
self.solver = solver
self.converged_reasons = {
0 : 'successful exit',
1 : 'number of iterations',
-1 : 'illegal input or breakdown',
}
@standard_call
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, context=None, **kwargs):
solver_kwargs = self.build_solver_kwargs(conf)
eps_a = get_default(eps_a, self.conf.eps_a)
eps_r = | get_default(eps_r, self.conf.eps_r) | sfepy.base.base.get_default |