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Fast Multipole Method (fast + multipole_method)

Distribution by Scientific Domains

Engineering	83%

Selected Abstracts

High order boundary integral methods forMaxwell's equations using Microlocal Discretization and Fast Multipole Methods

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
E. Darrigrand
An efficient method to solve time harmonic Maxwell's equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method (MLFMD) based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMD method. Moreover, we improve the MLFMD method by sparsifying the translation matrix of the MLFMM, which involves privileged directions in that application. This improvement leads to a significant reduction of the algorithm complexity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Fast multipole boundary element analysis of two-dimensional elastoplastic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007
P. B. Wang
Abstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Performance of a parallel implementation of the FMM for electromagnetics applications

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2003
G. Sylvand
Abstract This paper describes the parallel fast multipole method implemented in EADS integral equations code. We will focus on the electromagnetics applications such as CEM and RCS computation. We solve Maxwell equations in the frequency domain by a finite boundary-element method. The complex dense system of equations obtained cannot be solved using classical methods when the number of unknowns exceeds approximately 105. The use of iterative solvers (such as GMRES) and fast methods (such as the fast multipole method (FMM)) to speed up the matrix,vector product allows us to break this limit. We present the parallel out-of-core implementation of this method developed at CERMICS/INRIA and integrated in EADS industrial software. We were able to solve unprecedented industrial applications containing up to 25 million unknowns. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2003
Maurizio Cossi
Abstract The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in solution for any chemical system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A number of test applications are presented to evaluate the performances of the method. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 669,681, 2003 [source]

Shifted SSOR preconditioning technique for electromagnetic wave scattering problems

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2009
J. Q. Chen
Abstract To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations. The symmetric successive over-relaxation (SSOR) preconditioner is constructed based on the near-field matrix of the EFIE and employed to speed up the convergence rate of iterative methods. This technique can be greatly improved by shifting the near-field matrix of the EFIE with the principle value term of the magnetic field integral equation (MFIE) operator. Numerical results demonstrate that this method can reduce both the number of iterations and the computational time significantly with low cost for construction and implementation of preconditioners. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1035,1039, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24254 [source]