In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced...In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.展开更多
The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced ...The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).展开更多
This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels ar...This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels are considered.For non-oscillatory kernel,we outline the main ideas of the classical fast multipole method proposed by Greengard and Rokhlin.In the oscillatory case,the directional fast multipole method developed recently by Engquist and Ying is presented.展开更多
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations s...This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
We present a fast iterative solver for scattering problems in 2D,where a penetrable object with compact support is considered.By representing the scattered field as a volume potential in terms of the Green’s function...We present a fast iterative solver for scattering problems in 2D,where a penetrable object with compact support is considered.By representing the scattered field as a volume potential in terms of the Green’s function,we arrive at the Lippmann-Schwinger equation in integral form,which is then discretized using an appropriate quadrature technique.The discretized linear system is then solved using an iterative solver accelerated by Directional Algebraic Fast Multipole Method(DAFMM).The DAFMM presented here relies on the directional admissibility condition of the 2D Helmholtz kernel[1],and the construction of low-rank factorizations of the appropriate low-rank matrix sub-blocks is based on our new Nested Cross Approximation(NCA)[2].The advantage of the NCA described in[2]is that the search space of so-called far-field pivots is smaller than that of the existing NCAs[3,4].Another significant contribution of this work is the use of HODLR based direct solver[5]as a preconditioner to further accelerate the iterative solver.In one of our numerical experiments,the iterative solver does not converge without a preconditioner.We show that the HODLR preconditioner is capable of solving problems that the iterative solver can not.Another noteworthy contribution of this article is that we perform a comparative study of the HODLR based fast direct solver,DAFMMbased fast iterative solver,and HODLR preconditioned DAFMM based fast iterative solver for the discretized Lippmann-Schwinger problem.To the best of our knowledge,this work is one of the first to provide a systematic study and comparison of these different solvers for various problem sizes and contrast functions.In the spirit of reproducible computational science,the implementation of the algorithms developed in this article is made available at https://github.com/vaishna77/Lippmann_Schwinger_Solver.展开更多
The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to u...The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.展开更多
In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on ...In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.展开更多
A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to...A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.展开更多
At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise con...At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.展开更多
We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements...We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.展开更多
In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated wi...In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.展开更多
A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established usin...A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.展开更多
The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory req...The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O(N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.展开更多
The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods.In this article,following up on recent studies devoted to the formulation,implementation...The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods.In this article,following up on recent studies devoted to the formulation,implementation and evaluation of 3-D single-and multi-region elastodynamic fast multipole boundary element methods(FM-BEMs),a simple preconditioning strategy is proposed.Its efficiency is demonstrated on both the single-andmulti-region versions using benchmark examples(scattering of plane waves by canyons and basins).Finally,the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration(alpine basin of Grenoble,France),for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.展开更多
This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale (Hulikal et al., J. Mech. Phys. Solid...This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale (Hulikal et al., J. Mech. Phys. Solids 76, 144-161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally, while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study rough-surface adhesion.展开更多
We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level o...We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level of performance,capable of handling industrially-sized problems.The FFM avoids the implementation of a recursive tree and is a kernel independent algorithm.We give the algorithm and the relevant complexity estimates.The quasi-linear complexity enables the evaluation of convolution products with up to one billion entries.We illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of unknowns.Our implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.展开更多
This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann(AFMPB)solver.We introduce and discuss the following components in order:the Poi...This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann(AFMPB)solver.We introduce and discuss the following components in order:the Poisson-Boltzmann model,boundary integral equation reformulation,surface mesh generation,the nodepatch discretization approach,Krylov iterative methods,the new version of fast multipole methods(FMMs),and a dynamic prioritization technique for scheduling parallel operations.For each component,we also remark on feasible approaches for further improvements in efficiency,accuracy and applicability of the AFMPB solver to largescale long-time molecular dynamics simulations.The potential of the solver is demonstrated with preliminary numerical results.展开更多
Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries...Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries are close to each other.We present a boundary integralmethod in two dimensions which is specially designed tomaintain second order accuracy even if boundaries are arbitrarily close.Themethod uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy.For boundaries with many components we use the fast multipolemethod for efficient summation.We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium.We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals.Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region.A number of examples are presented.We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.展开更多
The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms o...The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.展开更多
基金the National Natural Science Foundation of China (No. 11074170)the Independent Research Program of State Key Laboratory of Machinery System and Vibration (SKLMSV) (No. MSV-MS-2008-05)the Visiting Scholar Program of SKLMSV (No. MSV-2009-06)
文摘In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.
文摘The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).
基金supported by the Sloan Foundation and the National Science Foundation of USA (CAREER Award DMS-0846501)
文摘This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels are considered.For non-oscillatory kernel,we outline the main ideas of the classical fast multipole method proposed by Greengard and Rokhlin.In the oscillatory case,the directional fast multipole method developed recently by Engquist and Ying is presented.
基金supported by the National Natural Science Foundation of China (11172291)the National Science Foundation for Post-doctoral Scientists of China (2012M510162)the Fundamental Research Funds for the Central Universities (KB2090050024)
文摘This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
基金the support of Women Leading IITM(India)2022 in Mathematics(SB22230053MAIITM008880)the support of Young Scientist Research Award from Board of Research in Nuclear Sciences,Department of Atomic Energy,India(No.34/20/03/2017-BRNS/34278)MATRICS grant from Science and Engineering Research Board,India(Sanction number:MTR/2019/001241).
文摘We present a fast iterative solver for scattering problems in 2D,where a penetrable object with compact support is considered.By representing the scattered field as a volume potential in terms of the Green’s function,we arrive at the Lippmann-Schwinger equation in integral form,which is then discretized using an appropriate quadrature technique.The discretized linear system is then solved using an iterative solver accelerated by Directional Algebraic Fast Multipole Method(DAFMM).The DAFMM presented here relies on the directional admissibility condition of the 2D Helmholtz kernel[1],and the construction of low-rank factorizations of the appropriate low-rank matrix sub-blocks is based on our new Nested Cross Approximation(NCA)[2].The advantage of the NCA described in[2]is that the search space of so-called far-field pivots is smaller than that of the existing NCAs[3,4].Another significant contribution of this work is the use of HODLR based direct solver[5]as a preconditioner to further accelerate the iterative solver.In one of our numerical experiments,the iterative solver does not converge without a preconditioner.We show that the HODLR preconditioner is capable of solving problems that the iterative solver can not.Another noteworthy contribution of this article is that we perform a comparative study of the HODLR based fast direct solver,DAFMMbased fast iterative solver,and HODLR preconditioned DAFMM based fast iterative solver for the discretized Lippmann-Schwinger problem.To the best of our knowledge,this work is one of the first to provide a systematic study and comparison of these different solvers for various problem sizes and contrast functions.In the spirit of reproducible computational science,the implementation of the algorithms developed in this article is made available at https://github.com/vaishna77/Lippmann_Schwinger_Solver.
基金Project supported by the National Basic Research Program of China(973 ProjectNo.2010CB832702)+4 种基金the National Science Funds for Distinguished Young Scholars of China(No.11125208)the National Natural Science Foundation of China(Nos.11125208 and 11302069)the 111 project under Grant B12032Jiangsu Province Graduate Students Research and Innovation Plan(No.KYZZ 0138)the scholarship from the China Scholarship Council(CSC)(No.201306710026)
文摘The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.
基金The project supported by the National Natural Science Foundation of China (10472051)
文摘In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.
文摘A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.
基金the support from the 2025 Henan Provincial Science and Technology Research Project,the Zhumadian 2023 Major Science and Technology Special Projectthe Postgraduate Education Reform and Quality Improvement Project of Henan Province.
文摘At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010MS080)the Research Fund for Doctoral Program of Higher Education of China (Grant No. 20070487403)
文摘We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.
基金This work is partially supported by Hong Kong Research Grants Council General Research Fund 604208 and the Nano Science and Technology Program at HKUST.
文摘In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.
基金supported by the National Natural Science Foundation of China(Grant No.10725210)the National Basic Research Program of China(Grant No.2009CB623200)
文摘A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.
文摘The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O(N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.
文摘The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods.In this article,following up on recent studies devoted to the formulation,implementation and evaluation of 3-D single-and multi-region elastodynamic fast multipole boundary element methods(FM-BEMs),a simple preconditioning strategy is proposed.Its efficiency is demonstrated on both the single-andmulti-region versions using benchmark examples(scattering of plane waves by canyons and basins).Finally,the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration(alpine basin of Grenoble,France),for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.
基金support for this study from the National Science Foundation of the United States (Grant EAR 1142183)the Terrestrial Hazards Observations and Reporting Center (THOR) at the California Institute of Technology
文摘This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale (Hulikal et al., J. Mech. Phys. Solids 76, 144-161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally, while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study rough-surface adhesion.
文摘We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level of performance,capable of handling industrially-sized problems.The FFM avoids the implementation of a recursive tree and is a kernel independent algorithm.We give the algorithm and the relevant complexity estimates.The quasi-linear complexity enables the evaluation of convolution products with up to one billion entries.We illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of unknowns.Our implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.
基金supported by NSF,DOE,HHMI,and NIH(B.Z./X.S./N.P.:NSF 0905164,B.Z./J.H.:NSF 0811130 and NSF 0905473,J.A.M.:NSF MCB1020765 and NIH GM31749)the NSF Center of Theoretical Biological Physics(CTBP)partially funded by the Chinese Academy of Sciences,the State Key Laboratory of Scientific/Engineering Computing,and the China NSF(NSFC1097218).
文摘This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann(AFMPB)solver.We introduce and discuss the following components in order:the Poisson-Boltzmann model,boundary integral equation reformulation,surface mesh generation,the nodepatch discretization approach,Krylov iterative methods,the new version of fast multipole methods(FMMs),and a dynamic prioritization technique for scheduling parallel operations.For each component,we also remark on feasible approaches for further improvements in efficiency,accuracy and applicability of the AFMPB solver to largescale long-time molecular dynamics simulations.The potential of the solver is demonstrated with preliminary numerical results.
文摘Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries are close to each other.We present a boundary integralmethod in two dimensions which is specially designed tomaintain second order accuracy even if boundaries are arbitrarily close.Themethod uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy.For boundaries with many components we use the fast multipolemethod for efficient summation.We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium.We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals.Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region.A number of examples are presented.We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.
基金supported by the US Army Ofce of Research(Grant No.W911NF11-1-0364)the National Science Foundation of USA(Grant No.DMS-1005441)National Natural Science Foundation of China(Grant No.91230105)
文摘The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.
