The very fast multipole method

The fast multipole method (FMM) has become an important alternative to traditional methods such as the Ewald method for computing the long-range interactions necessary to simulate charged or dipolar systems. In this paper, we present an improvement of this method, which we shall call the very fast multipole method (VFMM). The VFMM is shown to be a factor of about 1.2 faster than the FMM for two-dimensional systems and a factor about 2–3 times faster for three-dimensional systems without losing any accuracy for the worst case error.