Grid-Multipole Calculations

Abstract

We describe new high-order, momentum conserving methods for spreading charge to and interpolating potential from the mesh. These methods permit efficient grid-based algorithms to be used in high-order accurate n-body particle codes such as the fast multipole algorithm (FMM) of Greengard and Rokhlin [J. Comput. Phys., 73 (1987), pp. 325–348]. We report on experiments showing that potential evaluation using our spreading and interpolating techniques are significantly more accurate than evaluation using multipole expansions directly. We describe, briefly, how to incorporate our methods into the FMM.