Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-14T17:41:12.797Z Has data issue: false hasContentIssue false
  • English
  • Français

High-Accuracy Treecode Based on Pseudoparticle Multipole Method

Published online by Cambridge University Press:  26 May 2016

Atsushi Kawai  and
Junichiro Makino
Atsushi Kawai
Affiliation:
Computational Science Division, Advanced Computing Center, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama, 351-0198, Japan
Junichiro Makino
Affiliation:
Department of Astronomy, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We invented the pseudoparticle multipole method (P2M2), a method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we realized arbitrary-order treecode on MDGRAPE-2. Timing result shows MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) to 150 (for high accuracy). We parallelized the code so that it runs on MDGRAPE-2 cluster. The calculation speed of the code shows close-to-linear scaling up to 16 processors for N ≳ 106.

Type
Algorithms
Information
Symposium - International Astronomical Union , Volume 208: Astrophysical Supercomputing using Particle Simulations , 2003 , pp. 305 - 314
Copyright
Copyright © Astronomical Society of the Pacific 2003 

References

Athanassoula, E., Bosma, A., Lambert, J.-C., Makino, J. 1998, MNRAS, 293, 369 Google Scholar
Barnes, J. E. 1990, J. Comput. Phys., 87, 161 Google Scholar
Barnes, J. E., Hut, P. 1986, Nature, 324, 446 CrossRefGoogle Scholar
Fukushige, T., Ito, T., Makino, J., Ebisuzaki, T., Sugimoto, D., Umemura, M. 1991, PASJ, 43, 841 Google Scholar
Hernquist, L. 1990, ApJ, 356, 359 CrossRefGoogle Scholar
Hardin, R. H., Sloane, N. J. 1996, Discrete and Computational Geometry, 15, 429 Google Scholar
Kawai, A., Fukushige, F., Makino, J., Taiji, M. 2000, PASJ, 52, 659 CrossRefGoogle Scholar
Makino, J. 1990, J. Comput. Phys., 88, 393 CrossRefGoogle Scholar
Makino, J. 1991, PASJ, 43, 621 Google Scholar
Makino, J., Taiji, M., Ebisuzaki, T., Sugimoto, D. 1997, ApJ, 480, 432 CrossRefGoogle Scholar
Makino, J., Taiji, M. 1998, Scientific Simulations with Special-Purpose Computers — The GRAPE Systems (Chichester: John Wiley and Sons)Google Scholar
Makino, J. 1999, J. Comput. Phys., 151, 910 CrossRefGoogle Scholar
Narumi, T., Susukita, R., Koishi, T., Yasuoka, K., Furusawa, H., Kawai, A., & Ebisuzaki, T. 2000, in proceedings of SC2000 (ACM, in CD-ROM) Google Scholar
Sugimoto, D., Chikada, Y., Makino, J., Ito, T., Ebisuzaki, T., Umemura, M. 1990, Nature, 345, 33 Google Scholar