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A fast and accurate multigrid (MG) algorithm is presented for the direct method-of-moments (MoM) numerical simulation of radar scattering from large-scale one-dimensional (1-D) dielectric randomly rough surfaces. The proposed MG algorithm combines the desirable features of the generalized conjugate residual preconditioned iterative procedure and a parallel implementation of the spectral acceleration scheme proposed by Chou and Johnson. In addition, the paper proposes effective preconditioning schemes designed to further enhance the numerical efficiency of the proposed algorithm. The accelerated MG algorithm was benchmarked against the exact MG solution for both transverse electric and transverse magnetic polarizations. The efficiency of the proposed algorithm facilitates scattering calculations from electrically large surfaces. Hence, the algorithm was used to assess the performance of an approximate physical-optics scattering model used for ocean forward scattering simulations at the Johns Hopkins University Applied Physics Laboratory (JHU/APL). The validations are performed at X-band and W-band frequencies.Index Terms-Iterative schemes, method of moment (MoM), numerical methods, rough surface scattering, .