The volume integral equation in time-harmonic dielectric scattering.

Talk at the Workshop "BEM on the Saar". Saarbrücken University 2008

Martin Costabel

Slides Université de Rennes 1 (2008)

The problem of scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a volume integral equation. This integral equation is similar to the Lippmann-Schwinger integral equation in quantum-mechanical scattering which is also routinely used in acoustic scattering by a penetrable object. There the equation is a Fredholm integral equation of the second kind with a weakly singular kernel which can be treated numerically by various simple and efficient discretization methods. The peculiarity of the electromagnetic case is that the kernel is now strongly singular, and this means that the operator has a non-trivial essential spectrum. This essential spectrum, which is difficult to determine numerically, is now known, and in the talk we describe it for smooth and some non-smooth domains.

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