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A Finite-Element Method for Maxwell System Preserving Gauss Laws and Energy

Stéphanie Lala 1 Armel de Labourdonnaye
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We present a finite-element method for simulating the time domain Maxwell system in 3 dimensions for unstructured meshes. The geometrical approach of the equations of electromagnetism leads to consider the fields as exterior differential forms tied together by the operator of differentiation by Hodge operator. The spatial discretization uses mixed finite-elements, and the temporal one uses a leap-frog scheme. For this method we show the following properties : - it exactly preserves the Gauss laws and a discrete energy, - on a regular mesh, it amounts to a finite difference scheme which is of order 2 in space an time, - it preserves the Hamiltonian feature of Maxwell system which leads to interesting properties in long time computations. The method is numerically tested on cavity modes for cubes and homogeneous or heterogeneous spheres. The results are compared to exact solutions. The method is also compared to a finite volume based software.
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https://hal.inria.fr/inria-00073127
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Submitted on : Wednesday, May 24, 2006 - 11:56:28 AM
Last modification on : Friday, February 4, 2022 - 3:15:38 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:35:18 PM

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  • HAL Id : inria-00073127, version 1

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Stéphanie Lala, Armel de Labourdonnaye. A Finite-Element Method for Maxwell System Preserving Gauss Laws and Energy. RR-3557, INRIA. 1998. ⟨inria-00073127⟩

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