distributed lagrange multipliers based on fictitious domain method for second order elliptic problems in this article we further investigate the solution of linear second order elliptic boundary value problems by distributed lagrange multipliers based fictitious domain methods the following issues are addressed i derivation of the fictitious domain formulations ii finite element approximation iii iterative solution of the resulting finite dimensional problems of the saddle point type by preconditioned conjugate gradient and lanczos algorithms

adaptively weighted numerical integration in the finite cell method abstract with adaptively weighted aw numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis in this paper we demonstrate the application of aw integration scheme in the context of the finite cell method which must perform numerical integration over arbitrary domains without meshing the standard integration technique employed in fcm is the characteristic function method that converts the continuous integrand over a complex domain into a discontinuous integrand over a simple box domain then well known integrand adaptivity techniques are employed to integrate the resulting discontinuous integrand over the box domain although this method is simple to implement it becomes computationally very expensive for realistic complex 3d domains such as sculptures bones and engines in contrast in aw scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties in this paper we demonstrate the computational efficiency of aw over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions in addition aw offers a number of advantages including flexibility in the choice of quadrature points and basis functions

cauchy surfaces in a globally hyperbolic space time with the help of volume functions it is shown that a globally hyperbolic space time possesses a cauchy surface which is a three dimensional connected spacelike c hypersurface

the finite element immersed boundary method with distributed lagrange multiplier we introduce a new formulation for the finite element immersed boundary method which makes use of a distributed lagrange multiplier we prove that a full discretization of our model based on a semi implicit time advancing scheme is unconditionally stable with respect to the time step size

a spectral fictitious domain method with internal forcing for solving elliptic pdes a fictitious domain method is presented for solving elliptic partial differential equations using galerkin spectral approximation the fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes in the present study boundary constraints are enforced using lagrange multipliers and the novel aspect is that the lagrange multipliers are associated with smooth forcing functions compactly supported inside the fictitious domain this allows the accuracy of the spectral method to be preserved unlike the classical discrete lagrange multipliers method in which the forcing is defined on the boundaries in order to have a robust and efficient method equations for the lagrange multipliers are solved directly with an influence matrix technique using a fourier chebyshev approximation the high order accuracy of the method is demonstrated on one and two dimensional elliptic problems of second and fourth order the principle of the method is general and can be applied to solve elliptic problems using any high order variational approximation

buckling of unilaterally constrained columns by complementarity eigenvalue analyses abstract a numerical approach for the study of the elastic buckling of slender columns with unilateral supports is proposed this new approach is based on the numerical solution of a special type of eigenvalue problems that takes into account the complementarity character of the pair displacement obstacle reaction at each unilateral support the implementation of the proposed approach is illustrated by the determination of bifurcation loads and corresponding modes for several finite element models of columns

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

exact imposition of inhomogeneous dirichlet boundary conditions based on weighted finite cell method and level set function abstract the imposition of inhomogeneous dirichlet boundary conditions idbcs is essential in numerical analysis of a structure it is especially difficult and no longer straightforward whenever non conformal mesh is used to discretize a structure the original contribution of this paper is to develop a weighted finite cell method fcm with high computing accuracy the commonly used transfinite interpolation in the computer aided design cad community is now extended to define boundary value function so that the idbcs are imposed exactly unlike existing weak imposition forms and weighted interpolation methods it is shown that the weighting function and boundary value function involved in the weighted fcm can directly be applied to the physical field independently of the mesh discretization besides level set function lsf is used to represent the geometry of the considered physical domain to verify the effectiveness convergence performance and the generality of the proposed method numerical examples ranging from purely elastic to thermoelastic problems are illustrated computing results are compared with analytical and fea solutions

a fictitious domain approach with lagrange multiplier for fluid structure interactions we study a recently introduced formulation for fluid structure interaction problems which makes use of a distributed lagrange multiplier in the spirit of the fictitious domain method the time discretization of the problem leads to a mixed problem for which a rigorous stability analysis is provided the finite element space discretization is discussed and optimal convergence estimates are proved

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

shape topology optimization for navier stokes problem using variational level set method we consider the shape topology optimization of the navier stokes problem a new algorithm is proposed based on the variational level set method by this algorithm a relatively smooth evolution can be maintained without re initialization and drastic topology change can be handled easily finally the promising features of the proposed method are illustrated by two benchmark examples

shape optimization of dirichlet boundaries based on weighted b spline finite cell method and level set function abstract this paper addresses extended shape optimization problems where structural supports i e dirichlet boundaries and free boundaries are simultaneously optimized unlike traditional fem the weighted b spline finite cell method fcm is applied as structural analysis tool and combined with the level set function lsf to take into account dirichlet boundary condition dbc automatically through penalization of the displacement field the proposed shape optimization method achieves a comprehensive integration of fixed grid b spline shape function and level set function as both the structure and dirichlet boundaries are described in the form of lsf any modification of dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables meanwhile the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of dirichlet boundaries

on the spectral accuracy of a fictitious domain method for elliptic operators in multi dimensions this work is a continuation of the authors efforts to develop high order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach in a previous paper a new method was proposed based on the use of smooth forcing functions with identical shapes mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of lagrange multipliers in relation to a discrete set of boundary constraints for one dimensional elliptic problems this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth order algebraic convergence rate in this paper a spectrally accurate formulation is presented for multi dimensional applications instead of being specified locally the forcing function is defined as a convolution of a mollifier smooth bump function and a lagrange multiplier function the amplitude of the bump the multiplier function is then approximated by fourier series using a fourier galerkin approximation the spectral accuracy is demonstrated on a two dimensional laplacian problem and on a stokes flow around a periodic array of cylinders in the latter the numerical solution achieves the same high order accuracy as a stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

a distributed lagrange multiplier fictitious domain method for the simulation of flow around moving rigid bodies application to particulate flow in this article we discuss the application of a lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the navier stokes equations around moving rigid bodies the rigid body motion is due to hydrodynamical forces and gravity the solution method combines finite element approximations time discretization by operators splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method we conclude this article by the presentation of numerical results concerning the simulation of an incompressible viscous flow around a naca0012 airfoil with a fixed center but free to rotate then the sedimentation of circular cylinders in 2 d channels and finally the sedimentation of spherical balls in cylinders with square cross sections 2000 elsevier science s a all rights reserved

shell finite cell method a high order fictitious domain approach for thin walled structures abstract this article presents a generalization of the recently proposed finite cell method to thin walled structures this approach uses a combination of well known fictitious domain methods with high order hierarchical ansatz spaces known from the p version of the finite element method whereas the original concept embeds a three dimensional structure in a simple domain being meshed into a grid of cube shaped cells the extension presented in this paper applies the fictitious domain approach to a two dimensional master domain defined in the parameter plane of the geometric model implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach it is also remarked that the present approach can easily be carried over to isogeometric analysis opening an attractive possibility to simulate trimmed nurbs surfaces

mixed formulation for interface problems with distributed lagrange multiplier we study a mixed formulation for elliptic interface problems which has been recently introduced when dealing with a test problem arising from fluid structure interaction applications the formulation which involves a lagrange multiplier defined in the solid domain can be approximated by standard finite elements on meshes which do not need to fit with the interface in this paper we discuss a modification of the original formulation involving a different approach for the analysis and the numerical implementation of the lagrange multiplier new two dimensional numerical results confirm the good performances of the proposed schemes

an operator splitting scheme with a distributed lagrange multiplier based fictitious domain method for wave propagation problems we propose a novel fictitious domain method based on a distributed lagrange multiplier technique for the solution of the time dependent problem of scattering by an obstacle we study discretizations that include a fully conforming approach as well as mixed finite element formulations utilizing the lowest order nedelec edge elements in 2d on rectangular grids we also present a symmetrized operator splitting scheme for the scattering problem which decouples the operator that propagates the wave from the operator that enforces the dirichlet condition on the boundary of an obstacle a new perfectly matched layer pml model is developed to model the unbounded problem of interest this model is based on a formulation of the wave equation as a system of first order equations and uses a change of variables approach that has been developed to construct pml s for maxwell s equations we present an analysis of our fictitious domain approach for a one dimensional wave problem based on calculations of reflection coefficients we demonstrate the advantages of our fictitious domain approach over the staircase approximation of the finite difference method we also demonstrate some important properties of the distributed multiplier approach that are not shared by a boundary multiplier fictitious domain approach for the same problem numerical results for two dimensional wave problems that validate the effectiveness of the different methods are presented

a low numerical dissipation immersed interface method for the compressible navier stokes equations a numerical method to solve the compressible navier stokes equations around objects of arbitrary shape using cartesian grids is described the approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite difference discretization the method is suitable for compressible flows without shocks and can be classified as an immersed interface method the objects are sharply captured by the cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes located around the boundary in contrast with available methods no jump conditions are used or explicitly derived from the boundary conditions although a number of elements are adopted from previous immersed interface approaches a new element in the present approach is the use of the summation by parts formalism to develop stable non stiff first order derivative approximations at the irregular grid points second order derivative approximations as those appearing in the transport terms can be stiff when irregular grid points are located too close to the boundary this is addressed using a semi implicit time integration method moreover it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different mach and reynolds numbers

the finite cell method for linear thermoelasticity the recently introduced finite cell method fcm combines the fictitious domain idea with the benefits of high order finite elements while previous publications concentrated on single field applications this paper demonstrates that the advantages of the method carry over to the multi physical context of linear thermoelasticity the ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem a second example shows that the finite cell method correctly captures the thermoelastic state of a complex problem from engineering practice both examples additionally verify that also for two field problems dirichlet boundary conditions can be weakly imposed on non conforming meshes by the proposed extension of nitsche s method

fictitious domain finite element method for stokes elliptic interface problems with jump coefficients abstract in this paper the distributed lagrange multiplier fictitious domain dlm fd finite element method is studied for a generic stokes elliptic interface problem with jump coefficients which belongs to a type of linearized stationary fluid structure interaction problem a mixed finite element discretization is developed for the proposed dlm fd method for stokes elliptic interface problem and analyzed on the aspects of well posedness stability and optimal convergence numerical experiments are carried out and the theoretical error estimates of dlm fd finite element method are validated

geometric modeling isogeometric analysis and the finite cell method the advent of isogeometric analysis iga using the same basis functions for design and analysis constitutes a milestone in the unification of geometric modeling and numerical simulation however an important class of geometric models based on the csg constructive solid geometry concept such as trimmed nurbs surfaces do not fully support the isogeometric paradigm since basis functions do not explicitly represent the boundary the finite cell method fcm is a high order fictitious domain method which offers simple meshing of potentially complex domains into a structured grid of cuboid cells while still achieving exponential rates of convergence for smooth problems in the present paper we first discuss the possibility to directly couple the finite cell method to csg without any necessity for meshing the three dimensional domain and then explore a combination of the best of the two approaches iga and fcm closely following ideas of the recently introduced shell fcm the resulting finite cell extension to isogeometric analysis achieves a truly straightforward transfer of a trimmed nurbs surface into an analysis suitable nurbs basis while benefiting from the favorable properties of the high order and high continuity basis functions accuracy and efficiency of the new approach are demonstrated by a numerical benchmark and its versatility is outlined by the analysis of different trimmed design variants of a brake disk

coexisting equilibria and stability of a shallow arch unilateral displacement control experiments and theory the equilibria and stability of a shallow prestressed arch beam column are investigated theoretically and experimentally the deflection of the arch is unilaterally constrained by a displacement control device both snap through and remote coexisting equilibria are observed force deflection curves for primary and secondary equilibrium branches are measured for varying constraint locations the effect of the constraint location on the critical condition at which stability is lost resulting in a jump to a remote equilibrium is investigated good agreement is attained between experimental data and theoretical results based on minimization of the constrained strain energy and an inextensibility assumption

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs