Extension of the Spectral Acceleration Method to Lossy Medium and Its Application to Electromagnetic Scattering From Rough Surfaces

In the numerical analysis of electromagnetic scattering from random rough surfaces, the spectral acceleration (SA) algorithms proposed by Chou, Torrungrueng, and Johnson are very efficient in their capability of producing an O(N) iterative method of moment for 1-D lossless rough surfaces, where N is the number of surface unknowns. In this paper, we propose a method to extend the SA method to the lossy surfaces, where the magnitude of the complex radiation function may take noncanonical forms along the deformed integration path when evaluating the spectral representation of Green's function. The proposed method specifies ways on how the integration path in the complex angular plane should be deformed, how the domain of integration should be determined, and how the integration step size should be adjusted. It is shown to be very accurate through comparison with the exact results of Green's function. Its combination with the right-preconditioned generalized minimal residual (GMRES-RP) method renders an efficient and robust algorithm capable of handling both lossless and lossy rough surfaces. The predicted bistatic scattering coefficients agree almost perfectly with that of direct matrix inversion. The conservation of energy holds very well under a wide range of surface roughness and dielectric constant conditions. The proposed method thus provides a means for the analysis of scattering from rough surfaces, under realistic settings, and holds the potential for numerous important applications such as under surface target detection.