THEORETICAL AND COMPUTATIONAL ASPECTS OF SCATTERING FROM ROUGH SURFACES - ONE-DIMENSIONAL PERFECTLY REFLECTING SURFACES

We discuss the scattering of acoustic or electromagnetic waves from on e-dimensional rough surfaces. We restrict the discussion in this repor t to perfectly reflecting Dirichlet surfaces (TE polarization). The th eoretical development is for both infinite and periodic surfaces, the latter equations being derived from the former. We include both deriva tions for completeness of notation. Several theoretical developments a re presented. They are characterized by integral equation solutions fo r the surface current or normal derivative of the total field. All the equations are discretized to a matrix system and further characterize d by the sampling of the rows and columns of the matrix which is accom plished in either coordinate space (C) or spectral space (S). The stan dard equations are referred to here as CC equations of either the firs t (CC1) or second kind (CC2). Mixed representation, or SC-type, equati ons are solved as well as SS equations fully in spectral space. Comput ational results are presented for scattering from various periodic sur faces. The results include examples with grazing incidence, a very rou gh surface and a highly oscillatory surface. The examples vary over a parameter set which includes the geometrical optics regime, physical o ptics or resonance regime, and a renormalization regime. The objective of this study was to determine the best computational method for thes e problems. Briefly, the SC method was the fastest, but it did not con verge for large slopes or very rough surfaces for reasons we explain. The SS method was slower and had the same convergence difficulties as SC. The CC methods were extremely slow but always converged. The simpl est approach is to try the SC method first. Convergence, when the meth od works, is very fast. If convergence does not occur with SC, then SS should be used, and failing that CC.