Multilevel expansion of the sparse-matrix canonical grid method for two-dimensional random rough surfaces

The authors study simulations of 3D scattering and emission problems by using the sparse-matrix canonical grid (SMCG) method. The near interactions among the source points and field points are computed using the exact Green´s function. In contrast, the far interactions are computed by the fast Fourier transforms (FFTs) through a Taylor series expansion of the Green´ s function about a flat surface (z=O). The near interactions can be computed repeatedly in the iterative solution, or computed once and stored depending on the computer memory available, which will lead to low computation efficiency or large memory storage requirement. Therefore, the applicability of the SMCG method highly depends on the memory storage or the computation efficiency of computing the near interactions and the accuracy of the Taylor series expansion of the far interactions when the rms height of the rough surface increases. To overcome the iimitatjon of the SMCG method on the surface roughness, they demonstrated that a multilevel expansion can be employed for 1-D rough surface with large rms height. That is to say, they are not restricted to expand the Green´s function about the flat suface at z=0 as used in the SMCG method but about multilevel flat surfaces with different value of z with equal displacement In this paper, they extend this multilevei expansion approach to 2D perfect electric conductor and lossy dielectric surfaces