On the accuracy of the addition theorem for a scalar Green's function used in the FMM

Abstract

The addition theorem for a free-space scalar Green's function plays an important role in the fast multipole method (FMM). Therefore, both the accuracy and convergence are issues of concern in the code implementation of the FMM. In this paper, the addition theorem, when used in an unbounded Green's function, is numerically analyzed, and its accuracy is thus addressed and discussed. Specifically, the number of terms kept in the multipole expansion L is discussed in detail, and comparisons are made among the cases where difference parameters are used. A simple example applying the FMM to compute RCSs by a rectangular plate is given.