Multi-Trace M\"uller Boundary Integral Equation for Electromagnetic Scattering by Composite Objects

TL;DR

This paper develops a multi-trace boundary integral equation method for electromagnetic scattering by composite objects, improving computational efficiency and stability for complex dielectric structures.

Contribution

It extends the classical Müller equation to composite structures using the global multi-trace method with a novel extinction property, resulting in well-conditioned second-kind operators.

Findings

Accurate computation of field traces demonstrated

Method remains well-conditioned on dense meshes and low frequencies

Reduces computational costs for large-scale problems

Abstract

This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace method. The key ingredient enabling this extension is the use of the Stratton-Chu representation in complementary region, also known as the extinction property, which augments the off-diagonal blocks of the interior representation operator. The resulting block system is composed entirely of second-kind operators. A Petrov-Galerkin (mixed) discretization using Rao-Wilton-Glisson trial functions and Buffa-Christiansen test functions is employed, yielding linear systems that remain well conditioned on dense meshes and at low frequencies without the need for additional stabilization. This reduces computational costs associated with matrix-vector multiplications and iterative solving. Numerical experiments demonstrate the accuracy of the method in computing field traces and derived quantities.