In this paper,a new formulation is proposed to evaluate the origin intensity factors(OIFs)in the singular boundary method(SBM)for solving 3D potential problems with Dirichlet boundary condition.The SBM is a strong-for...In this paper,a new formulation is proposed to evaluate the origin intensity factors(OIFs)in the singular boundary method(SBM)for solving 3D potential problems with Dirichlet boundary condition.The SBM is a strong-form boundary discretization collocation technique and is mathematically simple,easy-to-program,and free of mesh.The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions.Traditionally,the inverse interpolation technique(IIT)is adopted to calculate the OIFs on Dirichlet boundary,which is time consuming for large-scale simulation.In recent years,the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary,but the Dirichlet problem remains an open issue.This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary.Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on inverse interpolation technique,the method of fundamental solutions,and the boundary element method.展开更多
In this paper,the recently-developed singular boundary method is applied to address free boundary problems.This mesh-less numerical method is based on the use of the origin intensity factors with fundamental solutions...In this paper,the recently-developed singular boundary method is applied to address free boundary problems.This mesh-less numerical method is based on the use of the origin intensity factors with fundamental solutions.Three numerical examples and their results are compared with the results obtained using traditional methods.The comparisons indicate that the proposed scheme yields good results in determining the position of the free boundary.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
In this paper,an improved singular boundarymethod(SBM),viewed as one kind of modified method of fundamental solution(MFS),is firstly applied for the numerical analysis of two-dimensional(2D)Stokes flow problems.The ke...In this paper,an improved singular boundarymethod(SBM),viewed as one kind of modified method of fundamental solution(MFS),is firstly applied for the numerical analysis of two-dimensional(2D)Stokes flow problems.The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives.The new contribution of this study is that the origin intensity factors for the velocity,traction and pressure are derived,and based on that,the SBM formulations for 2D Stokes flow problems are presented.Several examples are provided to verify the correctness and robustness of the presented method.The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.展开更多
基金The work described in this paper was supported by the National Science Funds for Distinguished Young Scholars of China(No.11125208)NSFC Funds(Nos.11302069,11372097,11602114 and 11662003)the 111 project under Grant No.B12032.
文摘In this paper,a new formulation is proposed to evaluate the origin intensity factors(OIFs)in the singular boundary method(SBM)for solving 3D potential problems with Dirichlet boundary condition.The SBM is a strong-form boundary discretization collocation technique and is mathematically simple,easy-to-program,and free of mesh.The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions.Traditionally,the inverse interpolation technique(IIT)is adopted to calculate the OIFs on Dirichlet boundary,which is time consuming for large-scale simulation.In recent years,the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary,but the Dirichlet problem remains an open issue.This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary.Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on inverse interpolation technique,the method of fundamental solutions,and the boundary element method.
基金supported by the National Natural Science Foundation of China(No.11702083)the open research fund of Guangxi key laboratory of water engineering materials and structures,Guangxi institute of water resources research(No.GXHRIWEMS-2019-05).
文摘In this paper,the recently-developed singular boundary method is applied to address free boundary problems.This mesh-less numerical method is based on the use of the origin intensity factors with fundamental solutions.Three numerical examples and their results are compared with the results obtained using traditional methods.The comparisons indicate that the proposed scheme yields good results in determining the position of the free boundary.
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 the National Basic Research Program of China(2010CB832702)the National Science Funds for Distinguished Young Scholars of China(11125208)+1 种基金the R&D Special Fund for Public Welfare Industry(Hydrodynamics,201101014)Programme of Introducing Talents of Discipline to Universities(111 project,Grant No.B12032).
文摘In this paper,an improved singular boundarymethod(SBM),viewed as one kind of modified method of fundamental solution(MFS),is firstly applied for the numerical analysis of two-dimensional(2D)Stokes flow problems.The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives.The new contribution of this study is that the origin intensity factors for the velocity,traction and pressure are derived,and based on that,the SBM formulations for 2D Stokes flow problems are presented.Several examples are provided to verify the correctness and robustness of the presented method.The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.
