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An augmented sparse-matrix canonical-grid (SMCG) approach for numerical analysis of scattering by dielectric random rough surfaces is developed. It is an extension of the previous modified SMCG scheme for perfect-electric-conducting (PEC) surfaces to dielectric cases, and is enhanced by adopting curved triangulation modeling. By using the curved modeling with curvilinear Rao-Wilton-Glisson basis functions (CRWG bases), the number of unknowns can be reduced substantially to extract results of the same accuracy, compared with using the planar triangular discretization with planar RWG bases. Numerical results for Gaussian and ocean-like dielectric rough surfaces are provided to confirm the validity and efficacy of the proposed method.