Performance of Preconditioned Nonstationary Methods for Electromagnetic Scattering From One Dimensional Dielectric Rough Surfaces

Abstract

For the analysis of electromagnetic scattering from one dimensional dielectric randomly rough surfaces, we apply the right-preconditioning technique to three nonstationary iterative algorithms, namely, the generalized minimal residual (GMRES), conjugate gradient squared (CGS), and biconjugate gradient stabilized (BiCGSTAB). The spectral acceleration technique is also utilized to expedite computation of matrix-vector product. Among the nonstationary methods considered, with the right-preconditioning (RP) applied, GMRES-RP is the most robust, followed by BiCGSTAB-RP, with CGS-RP falling behind. In terms of number of iterations to achieve convergence, for cases when they all converge, GMRES-RP requires the most whereas BiCGSTAB-RP the least, with CGS-RP slightly more demanding than BiCGSTAB-RP. However, in terms of run time, GMRES-RP is the most efficient, followed by BiCGSTAB-RP, and CGS-RP is the least efficient. This relative performance is in contrast to the unpreconditioned case as reported in the literature, which speaks of the impact of the adopted right-preconditioning on the spectral distribution of these nonstationary algorithms.