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Earth Science Informatics

, Volume 3, Issue 4, pp 289–296 | Cite as

Quasi-Monte Carlo integration on the grid for sensitivity studies

  • Emanouil Atanassov
  • Aneta Karaivanova
  • Todor Gurov
  • Sofiya IvanovskaEmail author
  • Mariya Durchova
  • Dimitar Sl. Dimitrov
Research Article

Abstract

In this paper we present error and performance analysis of quasi-Monte Carlo algorithms for solving multidimensional integrals (up to 100 dimensions) on the grid using MPI. We take into account the fact that the Grid is a potentially heterogeneous computing environment, where the user does not know the specifics of the target architecture. Therefore parallel algorithms should be able to adapt to this heterogeneity, providing automated load-balancing. Monte Carlo algorithms can be tailored to such environments, provided parallel pseudorandom number generators are available. The use of quasi-Monte Carlo algorithms poses more difficulties. In both cases the efficient implementation of the algorithms depends on the functionality of the corresponding packages for generating pseudorandom or quasirandom numbers. We propose efficient parallel implementation of the Sobol sequence for a grid environment and we demonstrate numerical experiments on a heterogeneous grid. To achieve high parallel efficiency we use a newly developed special grid service called Job Track Service which provides efficient management of available computing resources through reservations.

Keywords

Grid computing Quasi-Monte Carlo algorithms Sensitivity study 

References

  1. Al-Ali R, von Laszewski G, Amin K, Hategan M, Rana O, Walker D, Zaluzec N (2004) QoS support for high-performance scientific grid applications. In: Cluster IEEE international symposium on computing and the grid. CCGrid 2004, pp 134–143Google Scholar
  2. Atanassov E (2003) A new efficient algorithm for generating the scrambled Sobol’ sequence, numerical methods and applications. In: LNCS, vol 2542. Springer, pp 83–90Google Scholar
  3. Atanassov E, Karaivanova A, Gurov T, Ivanovska S, Durchova M (2009) Parallel quasi-Monte Carlo integration with application in environmental studies. In: Proceedings of SEE-GRID-SCI user forum, 9–10 Dec 2009. Istanbul, Turkey, pp 67–71Google Scholar
  4. Bird I, Jones B, Kee K (2009) The organization and management of grid infrastructures. IEEE Computer 42(1):36–46Google Scholar
  5. Bromley BC (1996) Quasirandom number generation for parallel Monte Carlo algorithms. J Parallel Distrib Comput 38(1):101–104CrossRefGoogle Scholar
  6. Caflisch R (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numer 7:1–49CrossRefGoogle Scholar
  7. Chaudhary S (2004) Acceleration of Monte Carlo methods using low discrepancy sequences. Dissertation, University of California, Los AngelesGoogle Scholar
  8. Chi H, Jones E (2007) Generating parallel quasirandom sequences by using randomization. J Parallel Distrib Comput 67(7):876–881CrossRefGoogle Scholar
  9. Chi H, Mascagni M (2007) Efficient generation of parallel quasirandom sequences via scrambling. In: LNCS, vol 4487. Springer, pp 723–730Google Scholar
  10. Czajkowski K, Fitzgerald S, Foster I, Kesselman C (2001) Grid information services for distributed resource sharing. In: Proceedings of the tenth IEEE international symposium on high-performance distributed computing (HPDC-10)Google Scholar
  11. Dimov I, Georgieva R, Ivanovska S, Ostromsky Tz, Zlatev Z (2009) Sensitivity analysis of air pollution models. In: BGSIAM’08 proceedings, pp 28–31. ISSN: 1313-3357Google Scholar
  12. Foster J, Kesselmann C (1998) The grid: blueprint for a new computing infrastructure. Morgan KaufmannGoogle Scholar
  13. Foster I, Kesselman C (2004) The grid: blueprint for a new computing infrastructure, 2nd edn. Morgan Kaufmann, pp 31–32Google Scholar
  14. Ivanovska S, Atanassov E, Karaivanova A (2005) A superconvergent Monte Carlo method for multiple integrals on the grid. In: LNCS, vol 3516. Springer, pp 735–742Google Scholar
  15. Khalili O, He J, Olschanowsky C, Snavely C, Casanova H (2006) Measuring the performance and reliability of production computational grids. In: Proceedings of the 7th IEEE/ACM international conference on grid computing, pp 293–300Google Scholar
  16. Kouvakis I, Georgatos F (2008) A report on the effect of heterogeneity of the grid environment on a grid job. In: Proc. LSSC 2007. LNCS, vol 4818. Springer, pp 476–483Google Scholar
  17. Large Hadron Collider in CERN (2010) http://en.wikipedia.org/wiki/Large_Hadron_Collider
  18. Misev A, Atanassov E (2008) Performance analysis of GRID middleware using process mining. In: Proc. 8th ICCS’08. LNCS 5101, Springer, pp 203–212Google Scholar
  19. Misev A, Atanassov E (2010) User level grid quality of service. In: Proc. 7th LNCS’09. To appear in LNCS, vol 5910. SpringerGoogle Scholar
  20. Monitoring EGEE Grid Infrastructure (2010) http://goc.grid.sinica.edu.tw/gstat
  21. Monitoring SEE-GRID Infrastructure (2010) http://goc.grid.sinica.edu.tw/gstat/seegrid
  22. Okten G, Tuffin B, Burago V (2006) A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance. J Complex 22(4):435–458CrossRefGoogle Scholar
  23. Ostromsky Tz, Zlatev Z (2007) Parallel and GRID implementation of a large scale air pollution model. In: Proc. NM&A’06. LNCS, vol 4310, pp 475–482. ISBN: 978-3-540-70940-4Google Scholar
  24. Owen A (2003) The dimension distribution and quadrature test functions. Stat Sin 13:1–17Google Scholar
  25. Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity snalysis in practice: a guide to assessing scientific models. WileyGoogle Scholar
  26. Saltelli A, Ratto M, Andres T, Compolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis. The Primer, WileyGoogle Scholar
  27. Schmid W, Uhl A (2001) Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Math Comp Sim 55:249–257CrossRefGoogle Scholar
  28. Soldatos J, Polymenakos L, Kormentzas G (2004) Programmable grids framework enabling QoS in an OGSA context. In: First international workshop on active and programmable grids architectures and components. 4th international conference in computer science ICCS 2004, June 6–9, 2004. Proceedings, Part III, vol 3038/2004. Krakow, Poland, pp 195–201Google Scholar
  29. SPRNG: scalable parallel random number generator (2010) http://sprng.cs.fsu.edu/
  30. The EGEE-III project website (2010) http://www.eu-egee.org
  31. The SEE-GRID-SCI project website (2010) http://www.see-grid-sci.eu

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Emanouil Atanassov
    • 1
  • Aneta Karaivanova
    • 1
  • Todor Gurov
    • 1
  • Sofiya Ivanovska
    • 1
    Email author
  • Mariya Durchova
    • 1
  • Dimitar Sl. Dimitrov
    • 1
  1. 1.Department of GRID Technologies and Applications, Institute for Parallel ProcessingBulgarian Academy of SciencesSofiaBulgaria

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