Simulation of wave scattering from rough surfaces using single integral equation and multilevel sparse-matrix canonical-grid method

There is an interest to simulate electromagnetic scattering from random rough surfaces, which finds applications in remote sensing of ocean, soil and ice. For analysis of a full vector wave scattering from a 2D dielectric random rough surface, two methods have been extensively investigated. One of these is based on the sparse-matrix canonical-grid (SMCG) strategy (see Tsang, L. et al., IEEE Trans. Antenna Propagat., vol.43, p.851-9, 1995; Pak, K. et al., J. Opt. Soc. Amer. A., vol.14, p.1515-29, 1997; Li, Q. et al., IEEE Trans. Antennas Propagat., vol.48, p.1-11, 2000). Traditionally, for simulation of scattering from a dielectric body, coupling equations are employed. Six surface unknowns at each surface point are used by the SMCG method. To reduce the number of surface unknowns and to alleviate the limitation on the surface roughness, a new algorithm based on a single integral equation formulation (see Yeung, M.S., IEEE Trans. Antennas Propagat., vol.47, no.10, p.1615-22, 1999) and a multilevel expansion version of the original SMCG method is developed. We make use of the Rao-Wilton-Glisson (RWG) triangular basis function that can better model the surface than the collocation method. Integration of the RWG basis function and the multilevel sparse-matrix canonical-grid method makes this single integral equation formulation suitable for simulation of scattering from a random surface of arbitrary roughness.