Comparison of iterative solvers for electromagnetic analysis of plasmonic nanostructures using multiple surface integral equation formulations

TL;DR

This paper compares the performance of four iterative solvers across five surface integral equation formulations for electromagnetic analysis of plasmonic nanostructures, providing guidelines for solver and formulation selection based on accuracy and computational resources.

Contribution

It offers a comprehensive comparison of iterative solvers and formulations for large-scale plasmonic problems, introducing practical guidelines for their selection.

Findings

GMRES and BICGSTAB perform best for large problems.

Formulation choice impacts convergence and accuracy.

Guidelines help optimize simulation efficiency and precision.

Abstract

The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a method of moments (MoM) methodology. In realistic large-scale optical problems, a direct inversion of the SIE-MoM matrix cannot be performed due to its large size, and an iterative solver must be used instead. This paper investigates the performance of four iterative solvers (GMRES, TFQMR, CGS, and BICGSTAB) for five different SIE-MoM formulations (PMCHWT, JMCFIE, CTF, CNF, and MNMF). Moreover, under this plasmonic context, a set of suggested guidelines are provided to choose a suitable SIE formulation and iterative solver depending on the desired simulation error and available runtime resources.