%0 Journal Article
%T Time harmonic wave diffraction problems in materials with sign-shifting coefficients
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Bonnet-Ben Dhia, Anne-Sophie
%A Ciarlet, Patrick
%A Zwölf, Carlo Maria
%< avec comité de lecture
%@ 0377-0427
%J Journal of Computational and Applied Mathematics
%I Elsevier
%V 234
%N 6
%P 1912-1919
%8 2010
%D 2010
%R 10.1016/j.cam.2009.08.041Journal articles
%X 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.
%G English
%L hal-00975073
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-00975073
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