Scattering by rough surface using a hybrid technique combining the multilevel UV method with the sparse matrix canonical grid method

A procedure is developed for combining efficiently the multilevel UV method with the sparse matrix canonical grid (SMCG) method in the computation of three-dimensional (3-D) wave scattering from random rough surface. It handles near- and intermediate-field interactions by the multilevel UV method and far-field interactions by the SMCG method. This hybrid UV/SMCG method removes the large memory requirement of both the UV method in the far field and the SMCG method in the near field. The computational complexity for the hybrid method is O(NlogN). The tradeoffs in computer memory requirement and CPU time between the UV part and the SMCG part are examined for Gaussian random rough surfaces with Gaussian correlation function and with exponential correlation function. For a surface area of 44 × 44 square wavelengths with RMS of 1 wavelength and 123,904 surface unknowns, the UV/SMCG method requires CPU of 52.2 s per iteration with total CPU of 46.6 min for 22 iterations on a single processor of CPU speed of 2.66 GHz.