Time-harmonic wave transmission problems with sign-shifting material coefficients

july, 2007
Publication type:
Conference without proceedings
Workshop:
8th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'07), Reading
Abstract:
Some electromagnetic materials present at a particular frequency an effective dielectric permittivity and/or magnetic permeability which are negative. We consider here a scalar model problem for the simulation of wave transmission between a classical material and a ``negative'' one. Introducing additional unknowns, we proposed in \cite{BoCZ07} some new variational formulations of this problem, which are of Fredholm type if the contrast of permittivity is large enough, and therefore suitable for a finite elements discretization. We prove here that, surprisingly, the natural variational formulation of the problem, although not ``coercive plus compact'', is also suitable for a finite elements discretization. Moreover, this numerical approach is less costly than the previous ones.
BibTeX:
@conference{Bon-Cia-Zwo-2007-1,
    author={Anne-Sophie Bonnet-BenDhia and Patrick Ciarlet and Carlo Maria 
           Zwölf },
    title={Time-harmonic wave transmission problems with sign-shifting 
           material coefficients },
    publisher={8th International Conference on Mathematical and Numerical 
           Aspects of Waves (WAVES'07), Reading },
    year={2007 },
    month={7},
}