Résolution des équations de Maxwell avec des éléments finis de Galerkin continus

Erell Jamelot 1
1 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 : Maxwell equations are easily solved when the computational domain is regular, but if it presents geometrical singularities (reentrant corners in 2D, reentrant corners and edges in 3D), the electromagnetic field is locally unbounded close to these singularities. We are interested in computing solutions to Maxwell equations in singular bounded domains with continuous finite elements. It allows to model communication devices such as wave-guides, stub filters. We first analyse the 2D quasi-electrostatic problem, in order to control space discretization. We present three (mixed) augmented methods, which show very convincing numerical results: - A refined version of the singular complement method (essential boundary conditions). - The weighted regularization method: Maxwell-Gauss equation is multiplied by a suitable weight, which depends on the distances to the geometrical singularities (essential boundary conditions). - The method with natural boundary conditions. We study then the extension of these methods to 3D domains. We give details of the resolution of time-dependent Maxwell equations in singular 3D domains with the weight regularization method, and we give original numerical results.
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  • HAL Id : tel-00440043, version 1



Erell Jamelot. Résolution des équations de Maxwell avec des éléments finis de Galerkin continus. Mathématiques [math]. Ecole Polytechnique X, 2005. Français. ⟨tel-00440043⟩



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