This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the...This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.展开更多
This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structu...This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structures,are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations.Bezier extraction technique is employed to accelerate the evaluation of NURBS basis functions.We adopt a radial integration method to address the additional domain integrals.The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis.展开更多
A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high comput...A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.展开更多
The localized method of fundamental solutions(LMFS)is a relatively new meshless boundary collocation method.In the LMFS,the global MFS approxima-tion which is expensive to evaluate is replaced by local MFS formulation...The localized method of fundamental solutions(LMFS)is a relatively new meshless boundary collocation method.In the LMFS,the global MFS approxima-tion which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains.The LMFS algorithm therefore converts differential equations into sparse rather than dense matrices which are much cheaper to calcu-late.This paper makes thefirst attempt to apply the LMFS,in conjunction with a domain-decomposition technique,for the numerical solution of steady-state heat con-duction problems in two-dimensional(2D)anisotropic layered materials.Here,the layered material is decomposed into several subdomains along the layer-layer inter-faces,and in each of the subdomains,the solution is approximated by using the LMFS expansion.On the subdomain interface,compatibility of temperatures and heatfluxes are imposed.Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate,stable and computationally efficient for the numerical solution of large-scale multi-layered materials.展开更多
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi...This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.展开更多
A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems.The method first discretizes the entire domain into a set of overlapping small subdomains,and then in ea...A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems.The method first discretizes the entire domain into a set of overlapping small subdomains,and then in each of the subdomains,the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method.The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations.The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries.Preliminary numerical experiments involving Poisson,Helmholtz,and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.展开更多
With the rapid development of computer technology,numerical simulation has become the third scientific research tool besides theoretical analysis and experi-mental research.As the core of numerical simulation,construct...With the rapid development of computer technology,numerical simulation has become the third scientific research tool besides theoretical analysis and experi-mental research.As the core of numerical simulation,constructing efficient,accurate and stable numerical methods to simulate complex scientific and engineering prob-lems has become a key issue in computational mechanics.The article outlines the ap-plication of singular boundary method to the large-scale and high-frequency acoustic problems.In practical application,the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency soundfield.This article focuses on the following two research areas.They are how to discretize partial differential equations into more appropriate linear equations,and how to solve linear equations more efficiently.The bottle neck problems encountered in the compu-tational acoustics are used as the technical routes,i.e.,efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies.The article reviews recent advances in emerging appli-cations of the singular boundary method for computational acoustics.This collection can provide a reference for simulating other more complex wave propagation.展开更多
The boundary particle method(BPM)is a truly boundary-only collocation scheme,whose basis function is the high-order nonsingular general solution or singular fundamental solution,based on the recursive composite multip...The boundary particle method(BPM)is a truly boundary-only collocation scheme,whose basis function is the high-order nonsingular general solution or singular fundamental solution,based on the recursive composite multiple reciprocity method(RC-MRM).The RC-MRM employs the high-order composite differential operator to solve a much wider variety of inhomogeneous problems with boundary-only collocation nodes while significantly reducing computational cost via a recursive algorithm.In this study,we simulate the Kirchhoff plate bending problems by the BPM based on the RC-MRM.Numerical results show that this approach produces accurate solutions of plates subjected to various loadings with boundary-only discretization.展开更多
基金supported by the National Science Fund of China(Grant No.12122205)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.
基金funded by National Natural Science Foundation of China(NSFC)under Grant Nos.11702238,51904202,and 11902212Nanhu Scholars Program for Young Scholars of XYNU.
文摘This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structures,are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations.Bezier extraction technique is employed to accelerate the evaluation of NURBS basis functions.We adopt a radial integration method to address the additional domain integrals.The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis.
基金supported by the National Natural Science Foundation of China(Nos.11872220,11772119)the Natural Science Foundation of Shandong Province of China(Nos.ZR2017JL004,2019KJI009)。
文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.
基金The work described in this paper was supported by the National Natural Science Foundation of China(Nos.11872220,11772119)the Natural Science Foundation of Shandong Province of China(Nos.2019KJI009,ZR2017JL004)+1 种基金the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009)the Key Laboratory of Road Construction Technology and Equipment(Chang’an University,Grant No.300102251505).
文摘The localized method of fundamental solutions(LMFS)is a relatively new meshless boundary collocation method.In the LMFS,the global MFS approxima-tion which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains.The LMFS algorithm therefore converts differential equations into sparse rather than dense matrices which are much cheaper to calcu-late.This paper makes thefirst attempt to apply the LMFS,in conjunction with a domain-decomposition technique,for the numerical solution of steady-state heat con-duction problems in two-dimensional(2D)anisotropic layered materials.Here,the layered material is decomposed into several subdomains along the layer-layer inter-faces,and in each of the subdomains,the solution is approximated by using the LMFS expansion.On the subdomain interface,compatibility of temperatures and heatfluxes are imposed.Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate,stable and computationally efficient for the numerical solution of large-scale multi-layered materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122205 and 11772119)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.
基金The work described in this paper was supported by the National Natural Science Foundation of China (Nos.11872220,12111530006)the Natural Science Foundation of Shandong Province of China (No.ZR2021JQ02)the Russian Foundation for Basic Research(No.21-51-53014).
文摘A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems.The method first discretizes the entire domain into a set of overlapping small subdomains,and then in each of the subdomains,the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method.The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations.The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries.Preliminary numerical experiments involving Poisson,Helmholtz,and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.
基金supported by China Postdoctoral Science Foundation(Grant No.2020M682335)Key R&D and Promotion Special Projects(Scientific Problem Tackling)in Henan Province of China(Grant No.212102210375).
文摘With the rapid development of computer technology,numerical simulation has become the third scientific research tool besides theoretical analysis and experi-mental research.As the core of numerical simulation,constructing efficient,accurate and stable numerical methods to simulate complex scientific and engineering prob-lems has become a key issue in computational mechanics.The article outlines the ap-plication of singular boundary method to the large-scale and high-frequency acoustic problems.In practical application,the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency soundfield.This article focuses on the following two research areas.They are how to discretize partial differential equations into more appropriate linear equations,and how to solve linear equations more efficiently.The bottle neck problems encountered in the compu-tational acoustics are used as the technical routes,i.e.,efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies.The article reviews recent advances in emerging appli-cations of the singular boundary method for computational acoustics.This collection can provide a reference for simulating other more complex wave propagation.
基金supported by a research project funded by the National Natural Science Foundation of China(Project No.10672051).
文摘The boundary particle method(BPM)is a truly boundary-only collocation scheme,whose basis function is the high-order nonsingular general solution or singular fundamental solution,based on the recursive composite multiple reciprocity method(RC-MRM).The RC-MRM employs the high-order composite differential operator to solve a much wider variety of inhomogeneous problems with boundary-only collocation nodes while significantly reducing computational cost via a recursive algorithm.In this study,we simulate the Kirchhoff plate bending problems by the BPM based on the RC-MRM.Numerical results show that this approach produces accurate solutions of plates subjected to various loadings with boundary-only discretization.
