Boosting the Maxwell double layer potential using a right spin factor
For researchers in computational electromagnetics, this provides a more stable and resonance-free formulation for solving Maxwell scattering problems on Lipschitz interfaces.
The paper constructs new spin singular integral equations for Maxwell scattering problems that improve condition numbers and eliminate spurious resonances compared to classical double layer potential methods.
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.