In this paper, we propose an iterative numerical approach based on the stochastic second degree (SSD) algorithm in combination with a new splitting of the impedance matrix to analyze electromagnetic scattering from 1-D dielectric rough surfaces. The embedded matrix-vector product is computed using the banded matrix iterative approach/canonical grid (BMIA/CAG) and the spectral acceleration (SA) technique. For Gaussian surface with Gaussian spectrum, through extensive numerical simulation, it is

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... bserved that for HH polarization, the proposed method requires roughly one half number of iterations as needed by the forward-backward method with spectral acceleration (FBM-SA). When the rms height is small, the proposed method takes more run time; when the rms slope is no less than 0.33 and rms height is no less than 1.0λ, where λ is the wavelength, the proposed method is more efficient. More importantly, it obviously improves the convergence properties over FBM-SA by changing cases from divergent to convergent when rms height is no less than 2.0λ and rms slope is no less than 0.55 except for one extreme case. For VV polarization, the proposed method is less computationally efficient in terms of run time and number of iterations than FBM-SA. However, as far as convergence properties are considered, similar to HH polarization, the proposed method improves over FBM-SA when the rms height and rms slope are large. Hence for both polarizations, the proposed method demonstrates its suitability when dealing with truly rough surfaces. Corresponding author: Y. Du (zjuydu03@zju.edu.cn).