Fast large scale full-wave multiple-scattering computation for three-dimensional random rough surfaces

Wave scattering from rough surfaces underpins a wide range of phenomena in microwaves, geoscience, optics, materials science, and plasmonic systems, yet remains challenging to model when surface roughness involves large root-mean-square (rms) heights, large slopes, or multiscale structure that lie beyond the validity of classical theories and the practical limits of existing numerical methods. We introduce a fast multilevel sparse-matrix canonical-grid (FML-SMCG) method that enables full-wave solutions of three-dimensional Maxwell's equations for scattering from three-dimensional rough surfaces. Using FML-SMCG, we perform full-wave simulations of dielectric rough surfaces with rms heights up to three wavelengths and surface areas as large as 256 wavelengths by 256 wavelengths, corresponding to approximately tenfold increases in roughness and sixteen-by-sixteen increases in simulated area relative to previous studies. We demonstrate the method through five representative examples of optical and microwave scattering, including enhanced backscattering and absorption from fractal surfaces, increased cross-polarized scattering from high-wind ocean surfaces, physical modeling of soil-surface scattering at L band (1.41 GHz), and scattering from soil surfaces beneath snow at frequencies up to Ku band (17.2 GHz). The FML-SMCG framework provides a general computational approach for studying wave interactions with rough surfaces across a broad range of physical regimes.