Second-kind boundary integral equations for electromagnetic scattering at composite objects

We consider electromagnetic scattering of time-harmonic fields in R3 at objects composed of several linear, homogeneous, and isotropic materials. Adapting earlier work on acoustic scattering (Claeys et al., 2015) we develop a novel second-kind direct boundary integral formulation for this scattering problem, extending the so-called Müller formulation for a homogeneous scatterer to composite objects. The new formulation is amenable to Galerkin boundary element discretization by means of discontinuous tangential surface vectorfields. A rigorous proof of its well-posedness is still missing. Yet numerical tests demonstrate excellent stability and competitive accuracy of the new approach compared with a widely used direct Galerkin boundary element method based on a first-kind boundary integral formulation. For piecewise constant approximation our experiments also confirm fast convergence of GMRES iterations independently of mesh resolution.