The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering

The objective of this work is to solve the combined field integral equation (CFIE) using the enhanced SDFMM to analyse electromagnetic scattering from practical random rough surfaces. For scattering problems involving low grazing incident waves, we found that the CFIE converges very fast compared with the EFIE, which converges very slowly for the same problem. Scattering at low grazing angles requires modeling of an infinite rough surface by a finite surface large enough such that the incident antenna beam excites no edge currents. In order to thoroughly investigate such a special scattering problem, a Monte Carlo simulation using many random surface realizations should be conducted which necessitates a fast converging and accurate technique such as the enhanced as SDFMM.