Transformations that Produce a Sparse Moment Method Matrix

Abstract

Previous moment method calculations (based on integral equations) have generally required utilizing a full N x N matrix when there are N unknowns. In this paper, novel basis and testing functions are presented for which the resulting matrix is approximately sparse when N is large, provided that the scatterer contains "smooth" regions. That is, nearly all of the matrix elements are so small that they may be set equal to zero. The ways to develop such functions are considered in detail, as are their effect on the condition number of the resulting matrix. Numerical calculations elucidate the properties of the resulting matrix, while calculations of the Radar Cross Section (RCS) show good results when approximating these small elements by zero. The motivations for the choices of the functions considered are explained in detail, since even more effective choices of functions may remain to be discovered. This method reduces the storage requirements from Order N² to Order N for an N unknown problem, and also correspondingly reduces the execution time required.