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Domain Decomposition Methods for Electromagnetic Wave Propagation Problems in Heterogeneous Media and Complex Domains

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Domain Decomposition Methods in Science and Engineering XIX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 78))

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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Acknowledgments

This work was granted access to the HPC resources of CCRT under the allocation 2009-t2009065004 made by GENCI (Grand Equipement National de Calcul Intensif).

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Authors and Affiliations

  1. Laboratoire J.A. Dieudonné, CNRS UMR 6621, F-06108, Nice Cedex, France

    Victorita Dolean

  2. NACHOS Project-Team, INRIA Sophia Antipolis – Méditerranée Research Center, F-06902, Sophia Antipolis Cedex, France

    Mohamed El Bouajaji & Stéphane Lanteri

  3. Mathematics Section, University of Geneva, CH-1211, Geneva, Switzerland

    Martin J. Gander

  4. Laboratoire Ampère, CNRS UMR 5005, F-69134, Ecully Cedex, France

    Ronan Perrussel

Authors
  1. Victorita Dolean
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  2. Mohamed El Bouajaji
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  3. Martin J. Gander
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  4. Stéphane Lanteri
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  5. Ronan Perrussel
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Corresponding author

Correspondence to Stéphane Lanteri .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Xiangtan University, Xiangtan, 411105, China, People's Republic

    Yunqing Huang

  2. FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Berlin, Germany

    Ralf Kornhuber

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Olof Widlund

  4. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Jinchao Xu

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Dolean, V., Bouajaji, M.E., Gander, M.J., Lanteri, S., Perrussel, R. (2011). Domain Decomposition Methods for Electromagnetic Wave Propagation Problems in Heterogeneous Media and Complex Domains. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_2

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