Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle

P. A. Martina1 and Petri Olaa2

a1 Department of Mathematics, University of Manchester, Manchester M13 9PL, England, U.K.

a2 Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland


Time-harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle. The corresponding electromagnetic transmission problem is reduced to a single integral equation over S for a single unknown tangential vector field, where S is the interface between the obstacle and the surrounding medium. In fact, several different integral equations are derived and analysed, including two previously-known equations due to E. Marx and J. R. Mautz, and two new singular integral equations. Mautz's equation is shown to be uniquely solvable at all frequencies. A new uniquely solvable singular integral equation is also found. The paper also includes a review of methods using pairs of coupled integral equations over S. It is these methods that are usually used in practice, although single integral equations seem to offer some computational advantages.

(Received January 30 1992)