Fast algorithm for the analysis of scattering by dielectric rough surfaces

A novel multilevel algorithm to analyze scattering from dielectric random rough surfaces is presented. This technique, termed the steepest-descent fast-multipole method, exploits the quasi-planar nature of dielectric rough surfaces to expedite the iterative solution of the pertinent integral equation. A combination of the fast-multipole method and Sommerfeld steepest-descent path integral representations is used to efficiently compute electric and magnetic fields that are due to source distributions residing on the rough surface. The CPU time and memory requirements of the technique scale linearly with problem size, thereby permitting the rapid analysis of scattering by large dielectric surfaces and permitting Monte Carlo simulations with realistic computing resources. Numerical results are presented to demonstrate the efficacy of the steepest-decent fast-multipole method. (C) 1998 Optical Society of America.