Novel multipole acceleration of forward-backward method for scattering from rough surfaces

A forward-backward method (F-BM) has been proposed to dramatically reduce the number of iterations in solving the matrix equation according to the scattering mechanisms of the one-dimensional rough surface, which requires only three or four iterations to obtain a vary accurate solution in many cases. However, its operational count, is still O(N/sup 2/) which has made this approach intractable for large-scale surface problems. We propose an approach to accelerate the forward-backward computation by using a spectral domain representation of the Green´s function. It is found that the operational count is only O(N) in the present approach which, in turn, makes the F-BM very fast (for example, 22.01 seconds CPU time to solve a matrix equation with 16384 unknowns on a 2048 /spl lambda/ long surface on the SGI workstation).