Numerical simulation of scattering from rough surfaces: a wavelet-based approach

Haar and B-spline wavelet basis functions are applied to the method of moments (MoM) in order to speed up the Monte Carlo simulation of scattering from rough surfaces. Application of wavelet basis functions in conjunction with imposed threshold levels produce sparse impedance matrices which are then solved efficiently using search routines such as the conjugate gradient method. These different threshold levels are imposed on matrix element values with respect to the element of largest magnitude in order to determine the accuracy versus computing speed criterion. Results are compared to previous results computed using a conventional pulse basis function and point matching as well as the existing theoretical solutions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time while providing very accurate results.