Multidimensional Monte Carlo Integration on Clusters with Hybrid GPU-Accelerated Nodes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8384)


The aim of this paper is to show that the multidimensional Monte Carlo integration can be efficiently implemented on clusters with hybrid GPU-accelerated nodes using recently developed parallel versions of LCG and LFG pseudorandom number generators. We explain how to utilize multiple GPUs and all available cores of CPUs within a single node and how to extend computations on all available nodes of a cluster using MPI. The results of experiments performed on a Tesla-based GPU cluster are also presented and discussed.


Multidimensional integration Monte Carlo methods Parallelized pseudorandom number generators GPU clusters 


  1. 1.
    Kindratenko, V.V., Enos, J., Shi, G., Showerman, M.T., Arnold, G.W., Stone, J.E., Phillips, J.C., mei Hwu, W.: GPU clusters for high-performance computing. In: Proceedings of the 2009 IEEE International Conference on Cluster Computing, pp. 1–8, New Orleans, LA, USA. IEEE, 31 Aug–4 Sept 2009Google Scholar
  2. 2.
    Bueno, J., Planas, J., Duran, A., Badia, R., Martorell, X., Ayguade, E., Labarta, J.: Productive programming of GPU clusters with OmpSs. In: 26th International Conference on Parallel Distributed Processing Symposium (IPDPS), 2012, pp. 557–568. IEEE (2012)Google Scholar
  3. 3.
    Göddeke, D., Strzodka, R., Mohd-Yusof, J., McCormick, P.S., Buijssen, S.H.M., Grajewski, M., Turek, S.: Exploring weak scalability for FEM calculations on a GPU-enhanced cluster. Parallel Comput. 33(10–11), 685–699 (2007)CrossRefGoogle Scholar
  4. 4.
    Fatica, M.: Accelerating linpack with CUDA on heterogenous clusters. In: Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units, GPGPU 2009, pp. 46–51, Washington, DC, USA, 8 Mar 2009Google Scholar
  5. 5.
    NVIDIA Corporation: NVIDIA next generation CUDA compute architecture: Fermi. (2009)
  6. 6.
    NVIDIA Corporation: CUDA Programming Guide. NVIDIA Corporation. (2012)
  7. 7.
    Pacheco, P.: Parallel Programming with MPI. Morgan Kaufmann, San Francisco (1996)Google Scholar
  8. 8.
    Bull, J.M., Freeman, T.L.: Parallel globally adaptive quadrature on the KSR-1. Adv. Comput. Math. 2, 357–373 (1994)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Ferrenberg, A., Landau, D., Wang, Y.J.: Monte Carlo simulations: hidden errors from good random number generators. Phys. Rev. Lett. 69, 3382–3384 (1992)CrossRefGoogle Scholar
  10. 10.
    Mascagni, M., Srinivasan, A.: Algorithm 806: SPRNG: a scalable library for pseudorandom number generation. ACM Trans. Math. Softw. 26(3), 436–461 (2000)CrossRefGoogle Scholar
  11. 11.
    Mascagni, M., Srinivasan, A.: Corrigendum: Algorithm 806: SPRNG: a scalable library for pseudorandom number generation. ACM Trans. Math. Softw. 26(4), 618–619 (2000)CrossRefGoogle Scholar
  12. 12.
    Mascagni, M.: Parallel linear congruential generators with prime moduli. Parallel Comput. 24(5–6), 923–936 (1998)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Mascagni, M., Chi, H.: Parallel linear congruential generators with Sophie-Germain moduli. Parallel Comput. 30(11), 1217–1231 (2004)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Mascagni, M., Srinivasan, A.: Parameterizing parallel multiplicative lagged-Fibonacci generators. Parallel Comput. 30(5–6), 899–916 (2004)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Srinivasan, A., Mascagni, M., Ceperley, D.: Testing parallel random number generators. Parallel Comput. 29(1), 69–94 (2003)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Stpiczyński, P., Szałkowski, D., Potiopa, J.: Parallel GPU-accelerated recursion-based generators of pseudorandom numbers. In: Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 571–578, Wroclaw, Poland. IEEE Computer Society Press, 9–12 Sept 2012Google Scholar
  17. 17.
    Stpiczyński, P.: Solving linear recurrence systems on hybrid GPU accelerated manycore systems. In: Proceedings of the Federated Conference on Computer Science and Information Systems, Szczecin, Poland, pp. 465–470. IEEE Computer Society Press, 18–21 Sept 2011Google Scholar
  18. 18.
    Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Am. Math. Soc. 84, 957–1041 (1978)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Hahn, T.: CUBA–a library for multidimensional integration. Comput. Phys. Commun. 168, 78–95 (2005)CrossRefMATHGoogle Scholar
  20. 20.
    Lautrup, B.: An adaptive multi-dimensional integration procedure. In: Proceedings of the 2nd Colloquium on Advanced Methods in Theoretical Physics, MarseilleGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of MathematicsMaria Curie–Skłodowska UniversityLublinPoland

Personalised recommendations