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

Authors:
Eric T. Chung;Patrick Ciarlet, Jr.
Affiliations:
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region;POEMS Laboratory, CNRS-INRIA-ENSTA UMR 7231, ENSTA ParisTech, 32, Boulevard Victor, 75739 Paris Cedex 15, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 5
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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.