The numerical calculation of rough surface scattering by the conjugate gradient method

The conjugate gradient method has been used to compute the solutions of the magnetic field integral equation for two-dimensional, perfectly conducting, Gaussian, rough surfaces. For surfaces whose roughness is of similar order to the incident wavelength, the rate of convergence of the conjugate gradient method is controlled by the RMS surface slope. In some cases, solutions are obtained with a significant reduction in the computation that direct methods require. Using the solution, the scattered field in the vicinity of the surface was calculated, and it is shown that the scattered field satisfies the extinction theorem to a good approximation