Electromagnetic Scattering From Randomly Rough Surfaces Using the Stochastic Second-Degree Method and the Sparse Matrix/Canonical Grid Algorithm

In applying the magnetic field integration equation for the numerical study of electromagnetic wave scattering from 2-D perfectly electric conducting randomly rough surfaces, we propose to apply the stochastic second-degree (SSD) method to improve the asymptotic convergence rate of the discretized system by the method of moment, in conjunction with the highly efficient method for calculating the product of the impedance matrix and a vector embedded in the sparse matrix/canonical grid (SMCG) algorithm. The proposed method, applied to a new matrix-splitting scheme, can also appreciably reduce the memory requirement for the same neighborhood distance parameter rd, or it can enlarge rd for the same memory requirement as that of SMCG. The preliminary results show that the proposed method has encouraging potential for moderate rough surfaces and for cases with a large number of unknowns. Moreover, in our approach, the structure of the new splitting in conjunction with SSD is quite general, and the involved key computation, namely, the product of the impedance matrix and a vector, is independent of the specifics of the approximation schemes. Hence, the formulation can be extended to a variety of approximation schemes, such as the recent multilevel expansion algorithm of the SMCG method.