An Improved Fast Multipole Algorithm for Potential Fields

Abstract

A new version of the fast multipole method (FMM) for potential fields is presented. We introduce a new representation of potentials, in which most translation operators are diagonal. As a result, for double precision calculations in two dimensions we obtain an improvement of a factor of two to four 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.