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Méthodes de Galerkin Discontinu pour la résolution du système de Maxwell sur des maillages localement raffinés non-conformes

Abstract : This work consists in the elaboration of a method able to solve the time-domain Maxwell's equations on locally refined conforming or non-conforming grids. We present here a Discontinuous Galerkin method based on a centred mean approximation for the surface integrals and a second order leapfrog scheme for advancing in time. The resulting scheme is stable and conserves a discrete analogue of the electromagnetic energy. We introduce a set of basis functions well adapted to orthogonal grids. These functions are less costly than the P1 or Q1 functions. Moreover, they ensure the divergence conservation. We prove that the dispersion error do not vary with the ratio time step over space step. As a consequence, we do not have to introduce local time stepping in order to deal with locally refined grids. To deal efficiently with unbounded problems, we use the perfectly Matched Layer (PML). When the mesh is non-conforming, we propose to increase the degree of the approximation at subgrid interfaces in order to avoid reflections dues to the interfaces. Three-dimensional numerical results show that the method is very efficient even if the rate refinement is high.
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https://pastel.archives-ouvertes.fr/pastel-00000555
Contributor : Ecole Des Ponts Paristech <>
Submitted on : Friday, September 10, 2010 - 3:52:25 PM
Last modification on : Tuesday, April 24, 2018 - 1:29:38 PM
Long-term archiving on: : Saturday, December 11, 2010 - 2:27:07 AM

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  • HAL Id : pastel-00000555, version 1

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Nicolas Canouet. Méthodes de Galerkin Discontinu pour la résolution du système de Maxwell sur des maillages localement raffinés non-conformes. Mathématiques [math]. Ecole des Ponts ParisTech, 2003. Français. ⟨NNT : 2003ENPC0009⟩. ⟨pastel-00000555⟩

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