Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces

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Abstract
We describe the use of iterative techniques for the solution of the integral equation that arises in an exact treatment of scalar wave scattering from randomly rough surfaces. The surfaces vary in either one or two dimensions, and the special case of a Dirichlet boundary condition is treated. It is found that these techniques, particularly when preconditioning is applied, are much more efficient than direct inversion techniques. Moreover, convergence is obtained for rms roughness of the order of 1, so the techniques have applicability over a wide parameter regime. Convergence is always to the exact solution found by direct inversion, exceptly for cases of extremely large-scaled rms surface heights in which the iterative techniques fail. In addition, by monitoring the residuals in the iteration process, it is immediately clear if the iterative techniques are failing, or performing badly in any given case. Finally, numerical results are compared with existing data in the enhanced backscattering regime.