Robust GMRES recursive method for fast finite element analysis of 3D electromagnetic problems

✍ Scribed by P. L. Rui; R. S. Chen

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 284 KB
• Volume: 49
• Category: Article
• ISSN: 0895-2477
• DOI: 10.1002/mop.22333

✦ Synopsis

Abstract

A robust generalized minimal residual recursive (GMRESR) iterative method is proposed to solve a large system of linear equations resulting from the use of an un‐gauged vector‐potential formulation of finite element method (FEM). This method involves an outer generalized conjugate residual (GCR) method and an inner generalized minimal residual (GMRES) method, where the inner GMRES acts as a variable preconditioning for the outer GCR. The efficient implementation of symmetric successive overrelaxation (SSOR) preconditioned GMRESR (SSOR‐GMRESR) algorithm is described in details for complex coefficient matrix equation. On several three‐dimensional electromagnetic problems, the resulting SSOR‐GMRESR approach converges in CPU time, which is 14.2–71.3 times shorter with respect to conventional conjugate gradient (CG) approach. By comparison with other popularly preconditioned CG methods, the results demonstrate that SSOR‐GMRESR is especially effective and robust when the A‐V formulation of FEM is applied to solve large‐scale time harmonic electromagnetic field problems. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1010–1015, 2007; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22333