Multilevel Expansion of the Sparse-Matrix Canonical Grid Method for Two-Dimensional Random Rough Surfaces

Wave scattering from two-dimensional (2-D) random rough surfaces up to several thousand square wavelengths has been previously analyzed using the sparse-matrix canonical grid (SMCG) method. The success of the SMCG method highly depends on the roughness of the random surface for a given surface area. In this paper, we present a multilevel expansion algorithm to overcome this limitation. The proposed algorithm entails the use of a three-dimensional (3-D) canonical grid. This grid is generated by a uniform discretization of the vertical displacement along the height ( -axis) of the rough surface in addition to the uniform sampling of the rough surface along the plane. The Green’s function is expanded about the 3-D canonical grid for the far interactions. The trade-off in computer memory requirements and CPU time between the neighborhood distance and the number of discretization levels along the -axis are discussed for both perfectly electric conducting (PEC) and lossy dielectric random rough surfaces. Ocean surfaces of Durden–Vesecky spectrum with various bandlimits are also studied.