Generalized Electromagnetic Scattering in a Complex Geometry

Abstract

We consider generalized time-harmonic Maxwell's equations on a real manifold of arbitrary dimension. Since the field tensors have complex coefficients the manifold is endowed with complex tangent and cotangent bundles and a complex valued pseudo-Riemannian metric. The lack of geodesics in general forces us to a restricted and careful use of standard differential geometric methods. We apply our machinery to scattering by a bounded body. As the main result we prove that the existence and uniqueness of a solution to an exterior boundary value problem is independent of the metric. This study originates from the perfectly matched layer or PML technique in computational electromagnetics.