On the discretization of the integral equation describing scattering by rough conducting surfaces

Numerical simulations of scattering from one-dimensional (1-D) randomly rough surfaces with Pierson-Moskowitz (P-M) spectra show that if the kernel (or propagator) matrix with zeros on its diagonal is used in the discretized magnetic field integral equation (MFIE), the results exhibit an excessive sensitivity to the current sampling interval, especially for backscattering at low-grazing angles (LGA's). Though the numerical results reported in this paper were obtained using the method of ordered multiple interactions (MOMI), a similar sampling interval sensitivity has been observed when a standard method of moments (MoM) technique is used to solve the MFIE. A subsequent analysis shows that the root of the problem lies in the correct discretization of the MFIE kernel. We found that the inclusion of terms proportional to the surface curvature (regarded by some authors as an additional correction) in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect. By reviewing the discretization procedure for MFIE we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly. The recommended current sampling interval for scattering calculations with P-M surfaces is also given.