A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method

The forward-backward method with a novel spectral acceleration algorithm (FB/NSA) has been shown to be an extremely efficient iterative method of moments (MoM) for the computation of scattering from one-dimensional (1-D) perfect electric conducting (PEC) and impedance rough surfaces [1]. The NSA algorithm is employed to rapidly compute interactions between widely separated points in the conventional FB method and is based on a spectral domain representation of source currents and the associated Green's function. For fixed surface roughness statistics, the computational cost and memory storage of the FB/NSA method are O(N-tot) as the surface size increases, where N-tot is the total number of unknowns to be solved. This makes studies of scattering from large surfaces, required in low grazing-angle scattering problems, tractable. In this paper, the FB/NSA method is extended to analyze scattering from two-dimensional. (2-D) rough surfaces. The NSA algorithm for this case involves a double spectral integral representation of source currents and the 3-D free-space scalar Green's function. The coupling between two spectral variables makes the problem more challenging, and the efficiency improvements obtained for 2-D surfaces are appreciable but not as dramatic as those for 1-D surfaces. However, the computational efficiency of the FB/NSA method for 2-D rough surfaces remains O(N-tot) as one of the surface dimensions increases. Comparisons of numerical results between the conventional FB method and the FB/NSA method for large-scale PEC rough surfaces show that the latter yields identical results to the former with a reduction of CPU time and only a slight increase in memory storage. In addition, the numerical results of FB/NSA method are in good agreement with experimental data obtained from the University of Washington, Seattle, WA.