Potential Integral Equations in Electromagnetics

TL;DR

This paper introduces a new integral equation formulation for electromagnetic scattering that uses decoupled vector and scalar potentials satisfying Lorentz gauge, resulting in well-conditioned second-kind Fredholm integral equations.

Contribution

It presents a novel integral equation approach with decoupled potentials for improved low-frequency stability and better spectral properties in electromagnetic scattering problems.

Findings

The new formulation is well-conditioned due to second-kind Fredholm equations.

Decoupling potentials enhances low-frequency stability.

Spectral analysis shows improved operator properties.

Abstract

In this work, a new integral equation (IE) based formulation is proposed using vector and scalar potentials for electromagnetic scattering. The new integral equations feature decoupled vector and scalar potentials that satisfy Lorentz gauge. The decoupling of the two potentials allows low-frequency stability. The formulation presented also results in Fredholm integral equations of second kind. The spectral properties of second kind integral operators leads to a well-conditioned system.