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Parallelization of Computational Physics Algorithms

  • D. W. Heermann
  • A. N. Burkitt
Part of the Springer Proceedings in Physics book series (SPPHY, volume 45)

Abstract

We report on the parallelization of two widely used algorithms in computational physics: The local-update Metropolis Monte Carlo simulation of the Ising model and a cluster identification algorithm which is used for percolation or percolation-like problems. The algorithm for the identification of clusters for the percolation-like problems was tested on the Swendsen-Wang method for the simulation of the Ising model. Simulation results are presented for a quench from a disordered state to a state below the coexistence curve. We show that the resulting domain growth has an exponential instead of a power law. The simulations were carried out on a parallel computer based on the transputer concept with up to 128 processors. The performance data show that the algorithms can perform with a linear speed-up. A scaling law for the performance of geometric parallel algorithms is proposed and tested.

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References

  1. [1]
    K. Binder, editor. Monte Carlo Methods. Springer Verlag, Heidelberg, 1986.MATHGoogle Scholar
  2. [2]
    M. H. Kalos and P. A. Whitlock. Monte Carlo Methods. Volume 1, Wiley, New York, 1986.CrossRefMATHGoogle Scholar
  3. [3]
    D. W. Heermann. Computer Simulation Methods in Theoretical Physics. Springer Verlag, Heidelberg, 1986.Google Scholar
  4. [4]
    K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction. Springer Series in Solid-State Sciences 80, Springer Verlag, Heidelberg, 1988.Google Scholar
  5. [5]
    W. G. Hoover. Molecular Dynamics. Volume 258 of Led. Notes. Phys., Springer Verlag, Heidelberg, 1986.Google Scholar
  6. [6]
    D. W. Heermann and A. N. Burkitt. Parallel Algorithms and Computational Physics. Springer Verlag, Heidelberg, 1989 to appear.Google Scholar
  7. [7]
    D. W. Heermann and R. C. Desai. Comp. Phys. Commun. 50, 297 (1988).CrossRefADSGoogle Scholar
  8. [8]
    A. Samal and T. Henderson. International Journal of Parallel Programming 16, 341 (1987).CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    M. N. Barber, R. B. Pearson, J. L. Richardson, and D. Touissaint. Phys. Rev. B32, 1720 (1985).ADSGoogle Scholar
  10. [10]
    A. Hoogland, A. Campagner, and H. W. J. Blöte. Physica 132A, 457 (1985).CrossRefGoogle Scholar
  11. [11]
    R. W. Hockney and C. R. Jesshope. Parallel Computers. Adam Hilger, Bristol, 1981.MATHGoogle Scholar
  12. [12]
    R. W. Gostick. ICL Tech. J. 1, 116 (1979).Google Scholar
  13. [13]
    G. S. Pawley and G. W. Thomas. J. Comp. Phys. 47, 165 (1982).CrossRefADSGoogle Scholar
  14. [14]
    P. W. Fortuin and P. W. Kasteleyn. Physica (Utrecht) 57, 536 (1972).CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    R. H. Swendsen and J. -S. Wang. Phys. Rev. Lett. 58, 86 (1987).CrossRefADSGoogle Scholar
  16. [16]
    D. Stauffer. Introduction to Percolation Theory. Taylor and Francis, London, 1985.CrossRefMATHGoogle Scholar
  17. [17]
    J. Hoshen and R. Kopelman. Phys. Rev. B14, 3428 (1976).Google Scholar
  18. [18]
    J. Kertecz. private communication.Google Scholar
  19. [19]
    A. N. Burkitt and D. W. Heermann. Parallelization of a cluster algorithm. November 1988. Wuppertal Preprint (to appear in Comp. Phys. Commun.).Google Scholar
  20. [20]
    J. D. Gunton, M. san Miguel, and P. S. Sahni. In C. Domb and J. L. Lebowitz, editors, Phase Transitions and Critical Phenomena, Academic Press, New York, Vol. 8 1983.Google Scholar
  21. [21]
    K. Binder and D. W. Heermann. In R. Pynn and T. Skjeltrop, editors, Scaling Phenomena in Disordered Systems, Plenum Press, New York, 1985.Google Scholar
  22. [22]
    S. M. Allen and J. W. Cahn. Acta Metall 27, 1085 (1979).CrossRefGoogle Scholar
  23. [23]
    E. T. Gawlinski, M. Grant, J. D. Gunton, and K. Kaski. Phys. Rev. B31, 281 (1985).Google Scholar
  24. [24]
    O. G. Mouritsen. Phys. Rev. B32, 1632 (1985).Google Scholar
  25. [25]
    G. S. Grest, D. J. Srolovitz, and M. P. Anderson. Phys. Rev. Lett. 52, 1321 (1984).CrossRefADSGoogle Scholar
  26. [26]
    A. Milchev, K. Binder, and D. W. Heermann. Z. Phys. B63 - Condensed Matter, 521 (1986).Google Scholar
  27. [27]
    A. Sadiq and K. Binder. J. Stat. Phys. 35, 517 (1984).CrossRefADSMathSciNetGoogle Scholar
  28. [28]
    R. Toral, A. Chakrabarti, and J. D. Gunton. Phys. Rev. Lett. 60, 2311 (1988).CrossRefADSGoogle Scholar
  29. [29]
    T. M. Rogers, K. R. Elder, and R. C. Desai. Phys. Rev. B, (to be published).Google Scholar
  30. [30]
    G. F. Mazenko and O. T. Vails. Phys. Rev. Lett. 59, 680 (1987).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • D. W. Heermann
    • 1
    • 2
  • A. N. Burkitt
    • 1
  1. 1.Fachbereich 8: PhysikBergische UniversitätWuppertalFed. Rep. of Germany
  2. 2.Institut für PhysikUniversität MainzMainzFed. Rep. of Germany

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