Symmetric Coupling for Eddy Current Problems

In this paper a novel symmetric finite element method-boundary element method-coupling for the $\mathbf{E}$-based eddy current model is derived in a rigorous fashion. To that end, the properties of potentials and boundary integral operators arising from a Stratton--Chu-type representation formula for the electric field in the nonconducting region are thoroughly analyzed in a Hilbert-space setting. It yields a variational problem with symmetric bilinear form that is coercive in the natural function spaces. Unknowns are the electric field inside the conductor and the equivalent surface current related to the magnetic field. Existence and uniqueness of solutions and the convergence of a conforming finite element/boundary element Galerkin discretization immediately follows. In particular, schemes based on curl-conforming edge elements and divergence-conforming surface elements are examined, and some aspects of implementation are discussed.