Comparison of different separable basis functions for the application of the Method of Moments on rough surface scattering

The basis functions that are most commonly used in the method of moments (MoM) for the simulation of rough surface scattering have a small support in terms of the wavelength. Complementary, the density of points per wavelength in the surface mesh has to be high enough to guarantee a good accuracy and this implies a computational effort which can often be excessive. Several factors contribute directly to the number of unknowns of the matrix to be inverted in the MoM: the value of the permittivity for the medium below the surface for a dielectric case, its dimensionality and size and the incident or observation angle, depending on the active or passive character of the observables to be calculated. One way of overcoming the difficulty of the exponential growth of unknowns is to use basis functions with a global support over a region larger than a wavelength. If the basis functions are a good representation of the surface fields and currents, a fewer number of terms is needed to represent them than when using a basis of very localized functions. In this work we present an alternative to the classical method of moments with pulse functions and point matching, based on a spectral representation in terms of Bessel functions.