Edge-based BE-FE coupling for electromagnetics

Electromagnetic problems can be solved using the coupled boundary-element/finite-element (BE-FE) method, where the conducting and magnetic parts are discretized by finite elements and the surrounding space is described with the help of the boundary element method. In this paper, we propose a novel BE-FE coupling procedure for the solution of electromagnetic problems. Starting from the potential formulation we derive a representation formula in the BE domain in terms of differential forms. We discretize the corresponding boundary integral equation by the DeRham map which generalizes the classical point collocation and yields an alternative approach to the Galerkin BE method. The Cauchy data will be discretized by the first-order Whitney elements on the boundary. In the FE domain, we apply the Galerkin discretization scheme using the spatial first-order Whitney elements. The coupling of these methods will be described and the feasibility of the proposed method will be demonstrated by means of numerical examples