A combined steepest descent-fast multipole algorithm for the analysis of three-dimensional scattering by rough surfaces

The scattering of electromagnetic waves by random rough surfaces is a subject of great practical and intellectual interest. Applications include, but are not limited to, remote sensing, long-range communications, radio astronomy, medicine, and surface physics. Random surfaces also exhibit several interesting scattering and polarization characteristics, such as backscattering enhancement and the generation of localized modes. A host of numerical techniques exist for analyzing rough surfaces. However, it is only recently that the fast algorithms have been developed, enabling analysis of larger surfaces. An efficient algorithm of O(N) computational complexity is presented.