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Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains

Abstract : We are interested here in the numerical modeling of time-harmonic electromagnetic wave propagation problems in irregularly shaped domains and heterogeneous media. In this context, we are naturally led to consider volume discretization methods (i.e. finite element method) as opposed to surface discretization methods (i.e. boundary element method). Most of the related existing work deals with the second order form of the time-harmonic Maxwell equations discretized by a conforming finite element method [14]. More recently, discontinuous Galerkin (DG) methods have also been considered for this purpose. While the DG method keeps almost all the advantages of a conforming finite element method (large spectrum of applications, complex geometries, etc.), the DG method has other nice properties which explain the renewed interest it gains in various domains in scientific computing: easy extension to higher order interpolation (one may increase the degree of the polynomials in the whole mesh as easily as for spectral methods and this can also be done locally), no global mass matrix to invert when solving time-domain systems of partial differential equations using an explicit time discretization scheme, easy handling of complex meshes (the mesh may be a classical conforming finite element mesh, a non-conforming one or even a mesh made of various types of elements), natural treatment of discontinuous solutions and coefficient heterogeneities and nice parallelization properties.
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https://hal.archives-ouvertes.fr/hal-00515575
Contributor : Ronan Perrussel <>
Submitted on : Tuesday, September 7, 2010 - 2:20:46 PM
Last modification on : Wednesday, October 14, 2020 - 4:24:44 AM

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Victorita Dolean, Mohamed El Bouajaji, Martin Gander, Stephane Lanteri, Ronan Perrussel. Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. Domain Decomposition Methods in Science and Engineering XIX, Aug 2009, Zhangjiajie, China. pp.15-26, ⟨10.1007/978-3-642-11304-8_2⟩. ⟨hal-00515575⟩

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