A multi-trace Müller boundary integral equation for composite electromagnetic scattering

In this talk, Van Le Chien will present a boundary integral equation for time-harmonic electromagnetic scattering by objects composed of multiple homogeneous, isotropic dielectric materials. The formulation extends the classical Müller 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 null-field or extinction property, which augments the off-diagonal blocks of the interior representation operator. The resulting block system is composed entirely of second-kind operators.

The multi-trace framework enables a Petrov–Galerkin discretization of the proposed boundary integral equation, employing Raviart–Thomas basis functions for the unknowns and Buffa–Christiansen functions for testing. Numerical results demonstrate that the discrete linear systems remain well-conditioned and stable on dense meshes and at low frequencies without additional stabilization. This substantially reduces computational costs associated with matrix-vector multiplications and iterative solving. The main price to pay is an increase in the number of boundary integral operators that must be assembled as the number of materials grows.

A rigorous proof of continuous and discrete well-posedness is still an open question.