Electromagnetic scattering at composite objects: A novel multi-trace boundary integral formulation

Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic scattering at general penetrable composite obstacles. We propose a new first-kind boundary integral equation formulation following the reasoning employed in [X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zürich (2011)] for acoustic scattering. We call it multi-trace formulation, because its unknowns are two pairs of traces on interfaces in the interior of the scatterer. We give a comprehensive analysis culminating in a proof of coercivity, and uniqueness and existence of solution. We establish a Calderón identity for the multi-trace formulation, which forms the foundation for operator preconditioning in the case of conforming Galerkin boundary element discretization.