An Application of Sampling Theorem to Moment Method Simulation in Surface Scattering

Abstract

The method of moment (MoM) is a numerical procedure for solving the equation Lf = g, where L is a continuous linear operator, f is the unknown function to be determined and g is a known excitation. In essence, the procedure converts the linear equation into a matrix equation and determines the unknown function in the form of a set of samples of the function through matrix inversion. It is well known that the sampling theorem states that to completely represent a function, one requires a minimum of two samples per wavelength, when the basis function is the Sinc function. Thus, by choosing the Sinc function as the testing and basis function in MoM implementation, we should have the smallest possible size for the matrix. To test the above stated approach, we calculate the scattering coefficient from a 2-D rough surface with a Gaussian distribution. The standard point matching approach is also used so that comparisons can be made between the two results. By comparing these numerical calculations with the IEM model, it is found that to achieve the same degree of accuracy, the number of unknowns used in the point matching method is an order of magnitude more than when the Sinc function is used as the basis function. This reduction in matrix size is specially significant in a three dimensional surface scattering problem, because we shall be able to reduce the matrix size by two orders of magnitude