A general framework for the OSRC-preconditioned EFIE in computational electromagnetics

TL;DR

This paper investigates preconditioning strategies for the EFIE in computational electromagnetics, comparing two formulations and demonstrating the effectiveness of the Magnetic-to-Electric approach through numerical experiments.

Contribution

It provides a comprehensive analysis of OSRC-based preconditioners for EFIE, highlighting the practical advantages of the MtE formulation and offering implementation insights.

Findings

MtE formulation is a cost-effective preconditioner.

Numerical experiments validate the spectral and performance benefits.

Guidelines and improvements for practical implementation are proposed.

Abstract

This work presents a comprehensive study of preconditioning strategies for the Electric Field Integral Equation (EFIE) using On-Surface Radiation Condition (OSRC) operators. We examine two distinct formulations -- the Magnetic-to-Electric (MtE) and Electric-to-Magnetic (EtM) maps -- used to precondition the EFIE, and we analyze their spectral properties, discretization behavior, and numerical performance. A central objective is to bridge the gap between theoretical development and practical implementation, identifying the strengths and limitations of each approach. Through numerical experiments on smooth, closed geometries, we show that the MtE formulation stands out as a cost-effective preconditioner in the context of Boundary Element Methods. We also offer implementation guidelines and propose improvements to address existing challenges. These findings provide a valuable reference for researchers and practitioners working with preconditioned boundary integral formulations in computational electromagnetics.