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
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.