Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T11:54:22.669Z Has data issue: false hasContentIssue false
  • English
  • Français

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

Published online by Cambridge University Press:  26 February 2011

Steven R. Lustig ,
J.J. Cristy  and
D.A. Pensak
Steven R. Lustig
Affiliation:
Du Pont, Experimental Station Route 141, Wilmington, DE 19880-0356
J.J. Cristy
Affiliation:
Du Pont, Experimental Station Route 141, Wilmington, DE 19880-0356
D.A. Pensak
Affiliation:
Du Pont, Experimental Station Route 141, Wilmington, DE 19880-0356
Get access

Abstract

The fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale as O(N2). The FMM execution times scale as O(N) on sequential workstations and vector processors and asymptotically 0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 278: Symposium W – Computational Methods in Materials Science , 1992 , 9
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Greengard, L. and Rokhlin, V., Technical Report 459, Computer Science Department, Yale University, 1986; J. Comput. Phys. 73, 325 (1987); Chemica Scripta 2, A, 139 (1989).Google Scholar
2. Greengard, L., The Rapid Evaluation of Potential Fields in Particle Systems, (M.I.T. Press, Massachussetts, 1988).CrossRefGoogle Scholar
3. Zhao, F., Report TR-995, M.I.T. Artificial Intelligence Laboratory, 1987.Google Scholar
4. Greengard, L. and Gropp, W.D., Report RR-640, Yale University, 1988.Google Scholar
5. Zhao, F. and Johnsson, S., Report CS89-6, Thinking Machines Corp., 1989.Google Scholar