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Pré-Publication, Document De Travail Année : 2009

On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body

Résumé

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface Γ. In this paper, following an idea developped by R. Kleinman and P. Martin [18] for acoustic scattering problems, we consider methods for solving the dielectric scattering problem using a single integral equation over Γ for a single unknown density. One knows that such boundary integral formulations of the Maxwell equations are not uniquely solvable when the exterior wave number is an eigenvalue of an associated interior Maxwell boundary value problem. We obtain four different families of integral equations for which we can show that by choosing some parameters in an appropriate way, they become uniquely solvable for all real frequencies.
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Dates et versions

hal-00439221 , version 1 (06-12-2009)
hal-00439221 , version 2 (24-02-2011)

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Martin Costabel, Frédérique Le Louër. On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body. 2009. ⟨hal-00439221v1⟩
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