Boosting the Maxwell double layer potential using a right spin factor

TL;DR

This paper introduces new spin singular integral equations for Maxwell scattering problems that improve numerical stability and avoid spurious resonances by modifying the classical double layer potential approach.

Contribution

The paper develops a novel formulation of integral equations for Maxwell's equations using a right spin factor, enhancing condition numbers and eliminating spurious solutions.

Findings

Better condition numbers for integral equations

No spurious resonances in solutions

Applicable to Lipschitz interfaces and media with piecewise constant properties

Abstract

We construct new spin singular integral equations for solving scattering problems for Maxwell's equations, both against perfect conductors and in media with piecewise constant permittivity, permeability and conductivity, improving and extending earlier formulations by the author. These differ in a fundamental way from classical integral equations, which use double layer potential operators, and have the advantage of having a better condition number, in particular in Fredholm sense and on Lipschitz regular interfaces, and do not suffer from spurious resonances. The construction of the integral equations builds on the observation that the double layer potential factorises into a boundary value problem and an ansatz. We modify the ansatz, inspired by a non-selfadjoint local elliptic boundary condition for Dirac equations.