Computing electromagnetic eigenmodes with continuous Galerkin approximations. (English) Zbl 1194.78053

Summary: Costabel and Dauge proposed a variational setting to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, three computational strategies are then possible. The original method, which requires a parameterization of the variational formulation. The second method, which is based on an a posteriori filtering of the computed eigenmodes. And the third method, which uses a mixed variational setting so that all spurious modes are removed a priori. In this paper, we discuss the relative merits of the approaches, which are illustrated by a series of 3D numerical examples.


78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
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