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

  • Authors:

  • A. S. Bonnet-Ben Dhia;P. Ciarlet, Jr.;C. M. Zwölf

  • Affiliations:

  • POEMS Laboratory, CNRS-INRIA-ENSTA UMR 7231, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France;POEMS Laboratory, CNRS-INRIA-ENSTA UMR 7231, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France;POEMS Laboratory, CNRS-INRIA-ENSTA UMR 7231, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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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 @D 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.