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

The addition theorem for a five-space scalar Green's function plays an impo rtant role in the fast multipole method (FMM). Therefore, both the accuracy and convergence are issues of concern in the code implementation of the FM M. In this paper, the addition theorem, when used in an unbounded Green's f unction, is numerically, analyzed, and its accuracy is thus addressed and d iscussed. Specifically, the number of terms kept in the multipole expansion L is discussed in detail, and comparisons are made among the cases where d ifference parameters are used. A simple example applying the FMM to compute RCSs by a rectangular plate is given. (C) 2001 John Wiley & Sons, Inc.