Skip to main content

Parallel Implementation of the Heisenberg Model Using Monte Carlo on GPGPU

  • Conference paper
Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Abstract

The study of magnetic phenomena in nanometer scale is essential for development of new technologies and materials. It also leads to a better understanding of magnetic properties of matter. An approach to the study of magnetic phenomena is the use of a physical model and its computational simulation. For this purpose, in previous works we have developed a program that simulates the interaction of spins in three-dimensional structures formed by atoms with magnetic properties using the Heisenberg model with long range interaction. However, there is inherent high complexity in implementing the numerical solution of this physical model, mainly due to the number of elements present in the simulated structure. This complexity leads us to develop a parallel version of our simulator using General-purpose GPUs (GPGPUs). This work describes the techniques used in the parallel implementation of our simulator as well as evaluates its performance. Our experimental results showed that the parallelization was very effective in improving the simulator performance, yielding speedups up to 166.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Heisenberg, W.: J. Phys. 49, 619 (1928)

    Google Scholar 

  2. Peçanha, J., Campos, A., Pampanelli, P., Lobosco, M., Vieira, M., Dantas, S.: Um modelo computacional para simulação de interação de spins em elementos e compostos magnéticos. XI Encontro de Modelagem Computacional (2008)

    Google Scholar 

  3. Blelloch, G., Narlikar, G.: A practical comparison of n-body algorithms. In: Parallel Algorithms. Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence (1997)

    Google Scholar 

  4. Preis, T., Virnau, P., Paul, W., Schneider, J.J.: Gpu accelerated monte carlo simulation of the 2d and 3d ising model. Journal of Computational Physics 228(12), 4468–4477 (2009)

    Article  MATH  Google Scholar 

  5. Ising, E.: Beitrag zur Theorie der Ferromagnetismus. Z. Physik 31, 253–258 (1925)

    Article  Google Scholar 

  6. Konstantinova, E.: Theoretical simulations of magnetic nanotubes using monte carlo method. Journal of Magnetism and Magnetic Materials 320(21), 2721–2729 (2008)

    Article  Google Scholar 

  7. NVIDIA: Nvidia cuda programming guide. Technical report, NVIDIA Corporation (2007)

    Google Scholar 

  8. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087–1092 (1953)

    Article  Google Scholar 

  9. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  10. Nyland, L., Harris, M., Prins, J.: Fast n-body simulation with cuda. In: Nguyen, H. (ed.) GPU Gems 3. Addison Wesley Professional, Reading (August 2007)

    Google Scholar 

  11. Swendsen, R.H., Wang, J.S.: Nonuniversal critical dynamics in monte carlo simulations. Physical Review Letters 58(2), 86+ (1987)

    Article  Google Scholar 

  12. Fukui, K., Todo, S.: Order-n cluster monte carlo method for spin systems with long-range interactions. Journal of Computational Physics 228(7), 2629–2642 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Santos, E.E., Rickman, J.M., Muthukrishnan, G., Feng, S.: Efficient algorithms for parallelizing monte carlo simulations for 2d ising spin models. J. Supercomput. 44(3), 274–290 (2008)

    Article  MATH  Google Scholar 

  14. Harada, T., Tanaka, M., Koshizuka, S., Kawaguchi, Y.: Real-time particle-based simulation on gpus. In: SIGGRAPH 2007: ACM SIGGRAPH 2007 posters, p. 52. ACM, New York (2007)

    Google Scholar 

  15. Kipfer, P., Segal, M., Westermann, R.: Uberflow: a gpu-based particle engine. In: HWWS 2004: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware, pp. 115–122. ACM Press, New York (2004)

    Chapter  Google Scholar 

  16. Yang, J., Wang, Y., Chen, Y.: Gpu accelerated molecular dynamics simulation of thermal conductivities. J. Comput. Phys. 221(2), 799–804 (2007)

    Article  MATH  Google Scholar 

  17. Georgii, J., Echtler, F., Westermann, R.: Interactive simulation of deformable bodies on gpus. In: Proceedings of Simulation and Visualisation 2005, pp. 247–258 (2005)

    Google Scholar 

  18. Tomov, S., McGuigan, M., Bennett, R., Smith, G., Spiletic, J.: Benchmarking and implementation of probability-based simulations on programmable graphics cards. Computers and Graphics 29(1), 71–80 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Campos, A.M. et al. (2011). Parallel Implementation of the Heisenberg Model Using Monte Carlo on GPGPU. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21931-3_50

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21931-3_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21930-6

  • Online ISBN: 978-3-642-21931-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics