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

2010

Publication type:

Paper in peer-reviewed journals

Journal:

Journal of Computational and Applied Mathematics, vol. 234(6), pp. 1912-1919

HAL:

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.

BibTeX:

@article{Bon-Cia-Zwo-2010, author={Anne-Sophie Bonnet-BenDhia and Patrick Ciarlet and Carlo Maria Zwölf }, title={Time harmonic wave diffraction problems in materials with sign-shifting coefficients }, doi={10.1016/j.cam.2009.08.041 }, journal={Journal of Computational and Applied Mathematics }, year={2010 }, volume={234(6) }, pages={1912--1919}, }