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

Abstract

The three-dimensional scattering by rough surfaces is analyzed using a combined steepest descent-fast multipole method algorithm (SDFMM) technique. The feature of this approach are: advantage is taken of the fact that a rough surface is nearly planar to derive efficient numerical integration rules for the Sommerfield integral representation of the free space Green's function; the Hankel functions arising in such an integration are evaluated using a Fast Multiple Method (FMM)-like algorithm that is tailored towards rough surfaces; and the proposed algorithm has O(N) CPU time and storage requirements. The technique is numerically rigorous and its accuracy can be controlled as desired.