Monte Carlo simulations of wave scattering from lossy dielectric random rough surfaces using the physics-based two-grid method and the canonical-gridmethod

In using the method of moments to solve scattering by lossy dielectric surf aces, usually a single dense grid (SDG) with 30 points per wavelength is re quired for accurate results, A single coarse grid (SCG) of ten points per w avelength does not give accurate results. However, the central processing u nit (CPU) and memory requirements of SDG are much larger than that of SCG. In a physics-based two-grid method (PBTG) two grids are used: a dense grid and a coarse grid. The method is based on the two observations: 1) Green's function of the lossy dielectric is attenuative and 2) the free-space Green 's function is slowly varying on the dense grid. In this paper, the PBTG me thod is combined with the banded-matrix iterative approach/canonical grid m ethod to solve rough surface scattering problem for both TE and TM cases an d also for near grazing incidence. We studied cases of dielectric permittiv ities as high as 125 + i)epsilon(o) and incidence angle up to 85 degrees. S alient features of the numerical results are: 1) an SCG has poorer accuracy for TM case than TE case; 2) PBTG-banded-matrix iterative approach/canonic al grid BMIA/CAG method speeds up CPU and preserves the accuracy; it has an accuracy comparable to single dense grid and yet has CPU comparable to sin gle coarse grid; 3) PBTG-BMIA/CAG gives accurate results for emissivity cal culations and also for low grazing backscattering problems (LGBA); and 4) t he computational complexity and the memory requirements of the present algo rithm are O(N log(N)) and O(N), respectively, where N is the number of surf ace unknowns on the coarse grid.