METHOD OF MOMENTS AND THE USE OF MULTIPOLE EXPANSION

In electromagnetic boundary value problems integral equations involving the free space Green function for the Helmholtz equation often occur. Using the method of moments to numerically solve such an equation a matrix equation is obtained. The entries of the matrix are given as multidimensional integrals which in general have to be calculated numerically. This paper presents an efficient method to approximate the main Part of these integrals. The free space Green function is expanded in scalar spherical wave functions. The translation properties of these wave functions then imply that the matrix elements can be expressed as a series of multipole moments. The method is illustrated by an implementation in the static case and the computation of the capacitance of a square plate. Basis functions with the correct edge and corner behaviour are used. The calculations of the multipole moments are done analytically. Numerical results using the point-matching and Galerkin's method are presented.