High-order solutions of three-dimensional rough-surface scattering problems at high-frequencies. Part II: The vector electromagnetic case

We introduce a new numerical scheme for three-dimensional electromagnetic rough-surface scattering simulations with the capability of delivering very accurate results from low to high frequencies at a cost that is independent of the wavelength of radiation. The method is an extension of the ideas and techniques introduced in the first paper of this series (Waves in Random and Complex Media, 15 (2005), pp. 1–16) to the vector electromagnetic case, and it is based on the solution of an integral equation formulation of the scattering problem. As in the scalar case, the solution of the integral equation (i.e. the current) is expressed as a slow modulation of an oscillatory exponential of known phase, and explicit recursive formulae are derived for the successive terms in a series expansion of the slow envelope in inverse powers of the wavenumber. As we show, and in spite of the considerably more involved nature of the derivations and resulting formulae, the performance of the method retains the favourable characteristics that were demonstrated in the treatment of acoustic scattering problems. In particular, results with full double-precision accuracy are presented for various geometries, incidences and polarizations.

Acknowledgements

Fernando Reitich gratefully acknowledges support from the Air Force Office of Scientific Research (AFOSR) through contract No. FA9550-05-1-0019, from the Natural Science Foundation (NSF) through grant No. DMS-0311763, and from the Army High Performance Computing Research Center (AHPCRC) under Army Research Laboratory cooperative agreement number DAAD19-01-2-0014.