Open AccessPerformance analysis of parallel Krylov methods for solving boundary integral equations in electromagnetism
Author(s) -
Carpentieri B.
Publication year - 2007
Publication title -
communications in numerical methods in engineering
Language(s) - English
Resource type - Journals
eISSN - 1099-0887
pISSN - 1069-8299
DOI - 10.1002/cnm.920
Subject(s) - preconditioner , krylov subspace , discretization , generalized minimal residual method , integral equation , mathematics , computational electromagnetics , iterative method , galerkin method , electromagnetism , matrix (chemical analysis) , fast multipole method , boundary element method , computer science , mathematical optimization , mathematical analysis , multipole expansion , finite element method , physics , electromagnetic field , materials science , quantum mechanics , composite material , thermodynamics
With the advent of high‐performance parallel computers, boundary integral methods have received an increasing interest for the solution of electromagnetic scattering problems of electrically large objects. The Galerkin discretization of integral equations leads to dense and complex linear systems whose size increases linearly with the dimension of the scatterer and quadratically with the frequency of the illuminating radiation. For solving realistic high‐frequency problems, iterative Krylov methods can be a viable alternative to out‐of‐core direct methods provided they are used in combination with fast algorithms for the matrix–vector products and robust parallel preconditioners. In this paper, we present experiments with iterative Krylov solvers combined with an approximate inverse preconditioner and the fast multipole method for the matrix–vector products. Numerical results on a set of problems arising from realistics radar cross‐section calculations in industry illustrate the potential of the proposed strategy for solving large‐scale problems in electromagnetism. The research described in this paper has been developed in the framework of a joint collaboration between CERFACS (Toulouse), EADS‐CCR (Toulouse), INRIA‐CERMICS (Sophia Antipolis). Copyright © 2006 John Wiley & Sons, Ltd.