Continuous Galerkin Methods for Solving Maxwell Equations in 3D Geometries

Maxwell equations are easily resolved when the computational domain is convex or with a smooth boundary, but if on the contrary it includes geometrical singularities, the electromagnetic field is locally unbounded and globally hard to compute. The challenge is to find out numerical methods which can capture the EM field accurately. Numerically speaking, it is advised, while solving the coupled Maxwell-Vlasov system, to compute a continuous approximation of the field. However, if the domain contains geometrical singularities, continuous finite elements span a strict subset of all possible fields, which is made of the H 1-regular fields. In order to recover the total field, one can use additional ansatz functions or introduce a weight. The first method, known as the singular complement method [4, 3, 14, 2, 9, 15, 16] works well in 2D and 2D½ geometries and the second method, known as the weighted regularization method [13] works in 2D and 3D. In this contribution, we examine some recent developments of the latter method to solve instationary Maxwell equations and we provide numerical results.