An efficient algorithm for wave scattering from two-dimensional lossy rough surfaces is proposed. It entails the use of a single magnetic field integral equation (SMFIE) in conjunction with a multilevel sparse-matrix canonical-grid (MSMCG) method. The Rao-Wilton-Glisson (RWG) triangular discretization is adopted to better model the rough surface than the pulse basis functions used in the well-established SMCG method. Using the SMFIE formulation, only one unknown per interior edge of the triangular mesh approximating the rough surface is required, and the iterative solution to the moment equation converges more rapidly than that of the conventional coupled equations for dielectric rough surfaces. The MSMCG method extends the applicability of the SMCG method to rougher surfaces. Parallel implementation of the proposed method enables us to model dielectric surfaces up to a few thousand square wavelengths. Simulation results are presented as bistatic scattering coefficients for Gaussian randomly rough surfaces.Index Terms-Multilevel sparse-matrix canonical-grid method (MSMCG), Rao-Wilton-Glisson (RWG) triangular basis, rough surface scattering, single magnetic field integral equation (SMFIE).

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