Convergence Property of IDR(s) Method Implemented along with Method of Moments for Solving Large-Scale Electromagnetic Scattering Problems Involving Conducting Objects

Abstract

In this paper, the performance of the induced dimension reduction (IDR) method implemented along with the method of moments (MoM) is described. The MoM is based on a combined field integral equation for solving large-scale electromagnetic scattering problems involving conducting objects. The IDR method is one of Krylov subspace methods. This method was initially developed by Peter Sonneveld in 1979; it was subsequently generalized to the IDR(s) method. The method has recently attracted considerable attention in the field of computational physics. However, the performance of the IDR(s) has hardly been studied or practiced for electromagnetic wave problems. In this study, the performance of the IDR(s) is investigated and clarified by comparing the convergence property and memory requirement of the IDR(s) with those of other representative Krylov solvers such as biconjugate gradient (BiCG) methods and generalized minimal residual algorithm (GMRES). Numerical experiments reveal that the characteristics of the IDR(s) against the parameter s strongly depend on the geometry of the problem; in a problem with a complex geometry, s should be set to an adequately small value in order to avoid the “spurious convergence” which is a problem that the IDR(s) inherently holds. As for the convergence behavior, we observe that the IDR(s) has a better convergence ability than GPBiCG and GMRES(m) in a variety of problems with different complexities. Furthermore, we also confirm the IDR(s)'s inherent advantage in terms of the memory requirements over GMRES(m).