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 observed that for HH polarization, the proposed method is slightly less computationally efficient in terms of run time and number of iterations than its counterpart without the SSD algorithm. However, the proposed method obviously improves the convergence properties over its counterpart by changing cases from divergent to convergent when the rms height and rms slope are large. For VV polarization, the relative performance in terms of number of iterations of the proposed method shows appreciable improvement and becomes better starting from the rms slope of 0.55 uniformly across all rms heights. As far as the convergence properties are considered, the proposed method obviously improves over its counterpart for certain large rms slopes. In short, the proposed method demonstrates its superiority when dealing with truly rough surfaces.
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