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Boosting the Maxwell double layer potential using a right spin factor

Journal article
Authors Andreas Rosén
Published in Integral Equations and Operator Theory
Volume 91
Issue 3
ISSN 0378-620X
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1007/s00020-019-2527-...
Keywords Maxwell scattering, Singular integral equation, Clifford algebra, transmission problems, lipschitz, equations, operator, Mathematics
Subject categories Mathematics

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.

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