Improved Fast Multipole Algorithm for Potential Fields

摘要

A new version of the Fast Multipole Method (FMM) for potential fields ispresented. While the old FMM uses multipole expansions to represent potentials, we use specially designed basis functions, displaying much faster convergence. Furthermore, we introduce an intermediate representation, in which most translation operators are diagonal. As a result, in two dimensions we obtain an improvement of a factor of three to five in speed, compared to previously published algorithms; the improvement is expected to be much greater in three dimensions. The performance of the method is illustrated with several numerical examples. (AN).