On iterative approaches for electromagnetic rough-surface scattering problems

Iterative techniques developed for solving general systems of linear equations have been applied to systems resulting from electromagnetic rough-surface scattering problems. Previously used iterative procedures that model the multiple scattering of the electromagnetic energy are shown to be mathematically equivalent to the application of stationary iterative procedures to the system of equations resulting from the standard moment method. Convergence difficulties that are sometimes observed with these approaches are due to the inherent limitations of the stationary techniques. The performances of the stationary approaches are compared with that of several conjugate-direction-based nonstationary iterative procedures through the application to a series of scattering surfaces that yield rapidly changing conditioning of the moment method interaction matrix. The stationary algorithms give the quickest convergence when applied to the systems with the best conditioning, but the nonstationary techniques prove much more robust in other more ill-conditioned situations.