The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engin...The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.展开更多
An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To a...An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.展开更多
We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from th...We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from the recent secondkind boundary integral approach of[X.Claeys,and R.Hiptmair,and E.Spindler.A second-kind Galerkin boundary element method for scattering at composite objects.BIT Numerical Mathematics,55(1):33-57,2015]for pure transmission problems and extend it to settings with essential boundary conditions.Based on so-called global multipotentials,we derive variational second-kind boundary integral equations posed in L^(2)(S),where S denotes the union of material interfaces.To suppress spurious resonances,we introduce a combined-field version(CFIE)of our new method.Thorough numerical tests highlight the low andmesh-independent condition numbers of Galerkin matrices obtained with discontinuous piecewise polynomial boundary element spaces.They also confirm competitive accuracy of the numerical solution in comparison with the widely used first-kind single-trace approach.展开更多
基金support of the National Natural Science Foundation of China(12072011).
文摘The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.
基金Supported by the National Natural Science Foundation of China (10674109)the Doctorate Foundation of Northwestern Polytechnical University (CX200601)
文摘An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.
基金The authors would like to thank L.Kielhorn for his great support during the development of the code for the first-and second-kind formulation in BETL2[25]The work of E.Spindler was partially supported by SNF under grant 20021137873/1X.Claeys received support from the ANR Research Grant ANR-15-CE23-0017-01.
文摘We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from the recent secondkind boundary integral approach of[X.Claeys,and R.Hiptmair,and E.Spindler.A second-kind Galerkin boundary element method for scattering at composite objects.BIT Numerical Mathematics,55(1):33-57,2015]for pure transmission problems and extend it to settings with essential boundary conditions.Based on so-called global multipotentials,we derive variational second-kind boundary integral equations posed in L^(2)(S),where S denotes the union of material interfaces.To suppress spurious resonances,we introduce a combined-field version(CFIE)of our new method.Thorough numerical tests highlight the low andmesh-independent condition numbers of Galerkin matrices obtained with discontinuous piecewise polynomial boundary element spaces.They also confirm competitive accuracy of the numerical solution in comparison with the widely used first-kind single-trace approach.
