Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II

TL;DR

This paper introduces a novel integral representation for solving time harmonic Maxwell equations in media with piecewise constant properties, avoiding low frequency breakdown and spurious resonances, demonstrated through numerical examples.

Contribution

It develops a new integral representation that leads to a stable, resonance-free system for Maxwell equations in complex media, improving upon classical methods.

Findings

The method avoids low frequency breakdown.

It produces resonance-free solutions.

Numerical examples demonstrate effectiveness.

Abstract

In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a coupled system of Fredholm integral equations of the second kind for four scalar densities supported on the material interface. Like the classical Muller equation, it has no spurious resonances. Unlike the classical approach, however, the representation does not suffer from low frequency breakdown. We illustrate the performance of the method with numerical examples.