REGULARIZATION OF THE VOLUME INTEGRAL OPERATOR OF ELECTROMAGNETIC SCATTERING

Abstract

We consider the scattering of time-harmonic electromagnetic waves by a bounded, penetrable, homogeneous obstacle. This problem admits an equivalent formulation in terms of a strongly singular volume integral equation (VIE). In this paper, and for smooth interfaces, we construct a regularizer for the operator that describes the VIE, i.e., we give an explicit representation of an integral operator, which, applied to the VIE, transforms it into the form “identity plus a compact operator”. The employed strategy is inspired by the previous work (Costabel et al. 2012).