Application of iterative techniques for electromagnetic scattering from dielectric random and reentrant rough surfaces

Abstract

Stationary [e.g., forward-backward method (FBM)] and nonstationary [e.g., conjugate gradient squared, quasi-minimal residual, and biconjugate gradient stabilized (Bi-CGSTAB)] iterative techniques are applied to the solution of electromagnetic wave scattering from dielectric random rough surfaces with arbitrary complex dielectric constants. The convergence issues as well as the efficiency and accuracy of all the approaches considered in this paper are investigated by comparing obtained scattering (in the form of normalized radar cross section) and surface field values with the numerically exact solution, computed by employing the conventional method of moments. It has been observed that similar to perfectly and imperfectly conducting rough surface cases, the stationary iterative FBM converges faster when applied to geometries yielding best conditioned systems but exhibits convergence difficulties for general geometries due to its inherit limitations. However, nonstationary techniques are, in general, more robust when applied to arbitrarily general dielectric random rough surfaces, which yield more ill-conditioned systems. Therefore, they might prove to be more suitable for general scattering problems. Besides, as opposed to the perfectly and imperfectly conducting rough surface cases, the Bi-CGSTAB method and FBM show two interesting behaviors for dielectric rough surface profiles: 1) FBM generally converges for reentrant surfaces when the vertical polarization is considered and 2) the Bi-CGSTAB method has a peculiar convergence problem for horizontal polarization. Unlike the other nonstationary iterative techniques used in this paper, where a Jacobi preconditioner is used, convergent results are obtained by using a block-diagonal preconditioner.