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The Pseudoparticle Multipole Method

Junichiro Makino
Department of Astronomy, School of Science
The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan
and Atsushi Kawai
College of Arts and Science
The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan


Barnes-Hut (BH) treecode and Fast multipole method (FMM) are algorithms which can calculate the gravitational interaction between N particles in or time. Both methods were proposed in 1980s and the treecode has become commonly used in cosomlogical simulations and simulations of galactic dynamics, where required accracy was low. For simulations which require high accuracy, however, the treecode has not been used because the implementation of high-order treecode is complex and calculation cost is high.

In this paper, we describe a new approach to implement high-order treecode and FMM, which we call Pseudoparticle Multipole Method (). In this method, we represent the multipole expansion back again by particles. As a result, the translation formulae for expansion coefficients are greatly simplified. Moreover, with this new method we can use GRAPE to accelerate the evaluation of the multipole expansion. Compated to the program on a workstation, the treecode with GRAPE can achieve up to 100 times speedup.

Jun Makino
Wed Apr 14 20:49:22 JST 1999