Time harmonic wave diffraction problems in materials with sign-shifting coefficients

Anne-Sophie Bonnet-Ben Dhia 1 Patrick Ciarlet 1 Carlo Maria Zwölf 1
1 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 present, in a given frequency range, an effective dielectric permittivity and/or magnetic permeability which are negative. We are interested in the reunion of such a "negative" material and a classical one. More precisely, we consider here a scalar model problem for the simulation of a wave transmission between two such materials. This model is governed by a Helmholtz equation with a weight function in the ΔΔ principal part which takes positive and negative real values. Introducing additional unknowns, we have already proposed in Bonnet-Ben Dhia et al. (2006) [1] some new variational formulations of this problem, which are of Fredholm type provided the absolute value of the contrast of permittivities is large enough, and therefore suitable for a finite element discretization. We prove here that, under similar conditions on the contrast, the natural variational formulation of the problem, although not "coercive plus compact", is nonetheless suitable for a finite element discretization. This leads to a numerical approach which is straightforward, less costly than the previous ones, and very accurate.
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Submitted on : Monday, April 7, 2014 - 5:54:45 PM
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Anne-Sophie Bonnet-Ben Dhia, Patrick Ciarlet, Carlo Maria Zwölf. Time harmonic wave diffraction problems in materials with sign-shifting coefficients. Journal of Computational and Applied Mathematics, Elsevier, 2010, 234 (6), pp.1912-1919. ⟨10.1016/j.cam.2009.08.041⟩. ⟨hal-00975073⟩

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