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A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials

Eric T. Chung 1 Patrick Ciarlet 2, * 
* Corresponding author
2 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 : Some electromagnetic materials exhibit, in a given frequency range, effective dielectric permittivity and/or magnetic permeability which are negative. In the literature, they are called negative index materials, left-handed materials or meta-materials. We propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta-material. The method we investigate can be considered as an alternative method compared to the method presented by the second author and co-workers. In particular, we shall use the abstract framework they developed to prove well-posedness of the exact problem. We recast this problem to fit later discretization by the staggered discontinuous Galerkin method developed by the first author and co-worker, a method which relies on introducing an auxiliary unknown. Convergence of the numerical method is proven, with the help of explicit inf-sup operators, and numerical examples are provided to show the efficiency of the method.
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Submitted on : Wednesday, May 16, 2012 - 9:55:06 AM
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Eric T. Chung, Patrick Ciarlet. A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials. 2012. ⟨hal-00697755⟩

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