Experiments With Lanczos Biconjugate a-Orthonormalization Methods for Mom Discretizations of Maxwell's Equations

Abstract

Abstract-In this paper we consider a novel class of Krylov projection methods computed from the Lanczos biconjugate AOrthonormalization procedure for the solution of dense complex non-Hermitian linear systems arising from the Method of Moments discretization of Maxwell's equations. We report on experiments on a set of model problems representative of realistic radar-cross section calculations to show their competitiveness with other popular Krylov solvers, especially when memory is a concern. The results presented in this study will contribute to assess the potential of iterative Krylov methods for solving electromagnetic scattering problems from large structures enriching the database of this technology.

Symmetric Inverse-Based Multilevel Ilu Preconditioning for Solving Dense Complex Non-Hermitian Systems in Electromagnetics

“…The CORS iterative solver is a non-optimal Krylov subspace method developed from a variant of the nonsymmetric Lanczos procedure, and is based on cheap three-term vector recurrences. In the experiments reported in [26], it turned out to be the …”

A comparative study of iterative solutions to linear systems arising in quantum mechanics

“…The present paper is devoted to the development of iterative solutions to such problems. The focus of this paper is on experiments of various iterative methods applied to the above-mentioned problems in both situations of no preconditioning and simple diagonal preconditioning, hopefully to demonstrate the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods [4][5][6] to other classic and popular iterative methods [7] in the field of molecular dynamics.…”

A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems

“…To overcome these drawbacks, some authors [11][12][13][14] improved the BiCOR method. The CORS method and its preconditioned variants [15][16][17] are effective and robust for solving linear systems in electromagnetics, due to transpose-free, cheap memory, free parameter and combination with the multilevel fast multipole algorithm (MLFMA) [18]. Although as seen from numerical experiments in [3,15] the CORS method shows good convergence properties compared to other Krylov subspace methods in many applications, there are some situations where its residual convergence is still irregular.…”

“…The CORS method and its preconditioned variants [15][16][17] are effective and robust for solving linear systems in electromagnetics, due to transpose-free, cheap memory, free parameter and combination with the multilevel fast multipole algorithm (MLFMA) [18]. Although as seen from numerical experiments in [3,15] the CORS method shows good convergence properties compared to other Krylov subspace methods in many applications, there are some situations where its residual convergence is still irregular. In order to improve the irregular convergence behavior, Jing et al [2,3] developed the BiCORSTAB method with the similar deriving strategies to the BiCGSTAB method [8].…”