hal-00975073
https://hal-ensta-paris.archives-ouvertes.fr/hal-00975073
doi:10.1016/j.cam.2009.08.041
[ENSTA] ENSTA Paris
[CNRS] CNRS - Centre national de la recherche scientifique
[INRIA] INRIA - Institut National de Recherche en Informatique et en Automatique
[INRIA-SACLAY] INRIA Saclay - Ile de France
[INRIA_TEST] INRIA - Institut National de Recherche en Informatique et en Automatique
[TESTALAIN1] TESTALAIN1
[UMA_ENSTA] Unité de Mathématiques Appliquées (UMA)
[INRIA2] INRIA 2
Time harmonic wave diffraction problems in materials with sign-shifting coefficients
Bonnet-Ben Dhia, Anne-Sophie
Ciarlet, Patrick
Zwölf, Carlo Maria
ART
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.
2010
en
Journal of Computational and Applied Mathematics
Elsevier