粒子法における高速演算の方法

抄録

Fast summation algorithms for a particle simulation are presented. The diffusion velocity which appears in the vortex methods is treated as an example of rapidly decaying potential and the convection velocity as far field potential. Computational time is reduced from O(N²) to O(N), where N is the particle number, for the diffusion velocity and to O(N log N) for the convection velocity by the use of blocks with various widths which are arranged in a computational domain based on a simple strategy. Our method is applied to a simulation of heat-vortex interaction and it is shown that the theoretical efficiency is achieved in this practical use and that our code is well parallelized.