Coifman wavelets in 3D scattering from very rough surfaces

Scattering of electromagnetic waves from rough surfaces has been studied by analytical, experimental, and numerical means. In the numerical approaches, the Monte Carlo method has been used for decades employing the method of moments (MoM). Traditional MoM in conjunction with the Galerkin procedure requires that the computation time be on the order of n/sup 2/ for matrix filling and n/sup 3/ for matrix inversion if Gaussian elimination is employed. In this paper we employ the Coifman wavelets (Coiflets) which have compact supports, permit the multiresolution analysis (MRA) and form an orthonormal basis with zero moments, smoothness, and Dirac-/spl delta/-like property. The Coiflets reduce the matrix filling into O(n). In a benchmark case of a very rough surface with /spl sigma/ = 1/spl lambda/, /spl lscr/ = 2/spl lambda/, the matrix size has been reduced from 32,768 /spl times/ 32,768 to 8192 /spl times/ 8192. Numerical results agree well with the laboratory measurements. The backscattering enhancements axe observed for both the like- and crosspolarizations.