A Simple Formulation of the Fast Multipole Method: Pseudo-Particle Multipole Method

TL;DR

The paper introduces P2M2, a simplified approach using pseudo-particles for multipole expansion in fast multipole methods, enhancing implementation simplicity and computational efficiency.

Contribution

It proposes a novel pseudo-particle based multipole method that simplifies high-order multipole expansions in FMM and treecode.

Findings

Simplifies implementation of FMM and treecode with high-order multipole terms

Demonstrates high accuracy and reduced calculation cost

Effective when combined with specialized hardware like GRAPE

Abstract

We present the pseudo-particle multipole method (P2M2), a new method to handle multipole expansion in fast multipole method and treecode. This method uses a small number of pseudo-particles to express multipole expansion. With this method, the implementation of FMM and treecode with high-order multipole terms is greatly simplified. We applied P2M2 to treecode and combined it with special-purpose computer GRAPE. Extensive tests on the accuracy and calculation cost demonstrate that the new method is quite attractive.