Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements

Annalisa Buffa 1 Patrick Ciarlet 2 Erell Jamelot 2
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : 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. © Springer-Verlag 2009.
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Submitted on : Wednesday, October 16, 2013 - 3:07:51 PM
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Annalisa Buffa, Patrick Ciarlet, Erell Jamelot. Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements. Numerische Mathematik, Springer Verlag, 2009, 113 (4), pp.497-518. ⟨10.1007/s00211-009-0246-2⟩. ⟨hal-00873069⟩

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