Version Of Fast Multipole Method Research Articles

Fast Multipole Accelerated Boundary Integral Equation Method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium

AbstractIn this paper, we develop an efficient numerical method 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.

Revision of FMM–Yukawa: An adaptive fast multipole method for screened Coulomb interactions

FMM–Yukawa is a mathematical software package primarily for rapid evaluation of the screened Coulomb interactions of N particles in three dimensional space. Since its release, we have revised and re-organized the data structure, software architecture, and user interface, for the purpose of enabling more flexible, broader and easier use of the package. The package and its documentation are available at http://www.fastmultipole.org/, along with a few other closely related mathematical software packages.

AFMPB: An adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson–Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node–patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summary Program title: AFMPB: Adaptive fast multipole Poisson–Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson–Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node–patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson–Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix–vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

A Fortran program package is introduced for the rapid evaluation of the screened Coulomb interactions of N particles in three dimensions. The method utilizes an adaptive oct-tree structure, and is based on the new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related packages are also available at http://www.fastmultipole.org/. This paper is a brief review of the program and its performance. Program summaryProgram title: FMM-YukawaCatalogue identifier: AEEQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPL 2.0No. of lines in distributed program, including test data, etc.: 12 385No. of bytes in distributed program, including test data, etc.: 79 222Distribution format: tar.gzProgramming language: Fortran77 and Fortran90Computer: AnyOperating system: AnyRAM: Depends on the number of particles, their distribution, and the adaptive tree structureClassification: 4.8, 4.12Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation.Solution method: An adaptive oct-tree is generated, and a new version of fast multipole method is applied in which the “multipole-to-local” translation operator is diagonalized.Restrictions: Only three and six significant digits accuracy options are provided in this version.Unusual features: Most of the codes are written in Fortran77. Functions for memory allocation from Fortran90 and above are used in one subroutine.Additional comments: For supplementary information see http://www.fastmultipole.org/Running time: The running time varies depending on the number of particles (denoted by N) in the system and their distribution. The running time scales linearly as a function of N for nearly uniform particle distributions. For three digits accuracy, the solver breaks even with direct summation method at about N=750.

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

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 fiber-reinforced 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.

Application of new fast multipole boundary integral equation method to crack problems in 3D

Fast multipole method (FMM) has been developed as a technique to reduce the computational cost and memory requirements in solving large scale problems. This paper discusses an application of the new version of FMM to three-dimensional boundary integral equation method (BIEM) for crack problems for the Laplace equation. The boundary integral equation is discretised with collocation method. The resulting algebraic equation is solved with generalised minimum residual method (GMRES). The numerical results show that the new version of FMM is more efficient than the original FMM.