A Robust Preconditioned GMRES Method for Electromagnetic Scattering From Dielectric Rough Surfaces

In this paper, we propose a generalized minimal residual procedure which is right preconditioned with the forward-backward method (FBM) for the analysis of electromagnetic scattering from 1-D dielectric randomly rough surfaces. The spectral acceleration (SA) technique is also combined to expedite the computation of matrix-vector product. For lossy dielectric, the Green's function is attenuative and suitably truncated, without the need to apply the SA technique for the lower medium. The applied preconditioning transforms the original linear system from near singular to stable with a good condition number. The spectrum of the preconditioned matrix is found condensed in the vicinity of the point 1 in the complex plane, which speaks of the good approximation quality of the preconditioner to the original matrix. Moreover, the construction of the preconditioner does not require the knowledge of the distribution of the impedance matrix spectrum, which means that the proposed method can be used as a general purpose iterative solver. The proposed method has demonstrated the desirable properties of a numerical algorithm: robust and efficient. Regarding robustness, the proposed method significantly improves convergence over the FBM-SA, in particular, for exponentially correlated rough surfaces. Regarding efficiency, the proposed method runs two to four times faster than the FBM-SA for horizontal (HH) polarization, and is about twice faster for vertical (VV) polarization. These features indicate that the proposed method can be effectively used to analyze electromagnetic scattering from 1-D dielectric Gaussian surfaces with both Gaussian and exponential spectra.