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

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.