An operator preconditioned combined field integral equation for electromagnetic scattering

TL;DR

This paper develops an operator preconditioned combined field integral equation to improve the numerical stability and conditioning of electromagnetic scattering simulations involving perfect electric conductors with Lipschitz boundaries.

Contribution

It introduces a new variational formulation that addresses ill-conditioning and resonant frequency instability in electromagnetic scattering integral equations.

Findings

The proposed method yields well-conditioned matrices on fine meshes.

It eliminates instability at spurious resonant frequencies.

Numerical results confirm the effectiveness of the approach.

Abstract

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices} on fine meshes and instability at spurious resonant frequencies. The remedy to ill-conditioned matrices is operator preconditioning, and resonant instability is eliminated by means of a combined field integral equation. Exterior traces of single and double layer potentials are complemented by their interior counterparts for a purely imaginary wave number. We derive the corresponding variational formulation in the natural trace space for electromagnetic fields and establish its well-posedness for all wave numbers. A Galerkin discretization scheme is employed using conforming edge boundary elements on dual meshes, which produces well-conditioned discrete linear systems of the variational formulation. Some numerical results are also provided to support the numerical analysis.