, Volume 113, Issue 4, pp 497-518
Date: 14 Jul 2009

Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements

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A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with the help of a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, their method required a parameterization of the variational formulation. In order to avoid this difficulty, we use a mixed variational setting instead of the parameterization, which allows us to handle the divergence-free constraint on the field in a straightforward manner. The numerical analysis of the method is carried out, and numerical examples are provided to show the efficiency of our approach.