Boosting the Maxwell double layer potential using a right spin factor

• Published in: Integral equations and operator theory Vol. 91; no. 3; pp. 1 - 25
• Main Author: Rosén, Andreas
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2019; Springer Nature B.V
• Subjects: Analysis; Boundary conditions; Boundary value problems; Clifford algebra; Conductors; Electric double layer; equations; Formulations; Integral equations; lipschitz; Matematik; Mathematical analysis; Mathematics; Mathematics and Statistics; Maxwell scattering; operator; Operators (mathematics); Singular integral equation; Singular integral equations; transmission problems; Singular integral equation; 78M15; Clifford algebra; 45E05; 15A66; Maxwell scattering
• ISSN: 0378-620X; 1420-8989; 1420-8989
• DOI: 10.1007/s00020-019-2527-1

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.