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 (1D) perfect electric conducting (PEC) and impedance rough surfaces. 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 (2D) rough surfaces. The NSA algorithm for this case involves a double spectral integral representation of source currents and the 3D free-space scalar Green´s function. The coupling between two spectral variables makes the problem more challenging, and the efficiency improvements obtained for 2D surfaces are appreciable but not as dramatic as those for 1D surfaces. However, the computational efficiency of the FB/NSA method for 2D 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