Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method

Scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface is studied with the banded matrix iterative approach/canonical grid (BMIA/CAG) method. The BMIA/CAG is an improvement over the previous BMIA. The key idea of BMIA/CAG is that outside the near-field interaction, the rest of the interactions can be translated to a canonical grid by Taylor series expansion. The use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast Fourier transform for nonnear field interaction. The method can be used for Monte-Carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface. We illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns. The method is also applied to study scattering from random rough surfaces at near-grazing incidence. The numerical examples illustrate the importance of using a large surface length for some backscattering problems