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The volume integral equation in time-harmonic dielectric scattering.

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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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