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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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 134–143
Atanassov E (2003) A new efficient algorithm for generating the scrambled Sobol’ sequence, numerical methods and applications. In: LNCS, vol 2542. Springer, pp 83–90
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 67–71
Bird I, Jones B, Kee K (2009) The organization and management of grid infrastructures. IEEE Computer 42(1):36–46
Bromley BC (1996) Quasirandom number generation for parallel Monte Carlo algorithms. J Parallel Distrib Comput 38(1):101–104
Caflisch R (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numer 7:1–49
Chaudhary S (2004) Acceleration of Monte Carlo methods using low discrepancy sequences. Dissertation, University of California, Los Angeles
Chi H, Jones E (2007) Generating parallel quasirandom sequences by using randomization. J Parallel Distrib Comput 67(7):876–881
Chi H, Mascagni M (2007) Efficient generation of parallel quasirandom sequences via scrambling. In: LNCS, vol 4487. Springer, pp 723–730
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)
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: 1313-3357
Foster J, Kesselmann C (1998) The grid: blueprint for a new computing infrastructure. Morgan Kaufmann
Foster I, Kesselman C (2004) The grid: blueprint for a new computing infrastructure, 2nd edn. Morgan Kaufmann, pp 31–32
Ivanovska S, Atanassov E, Karaivanova A (2005) A superconvergent Monte Carlo method for multiple integrals on the grid. In: LNCS, vol 3516. Springer, pp 735–742
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 293–300
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 476–483
Large Hadron Collider in CERN (2010) http://en.wikipedia.org/wiki/Large_Hadron_Collider
Misev A, Atanassov E (2008) Performance analysis of GRID middleware using process mining. In: Proc. 8th ICCS’08. LNCS 5101, Springer, pp 203–212
Misev A, Atanassov E (2010) User level grid quality of service. In: Proc. 7th LNCS’09. To appear in LNCS, vol 5910. Springer
Monitoring EGEE Grid Infrastructure (2010) http://goc.grid.sinica.edu.tw/gstat
Monitoring SEE-GRID Infrastructure (2010) http://goc.grid.sinica.edu.tw/gstat/seegrid
MPI website (2010) http://www-unix.mcs.anl.gov/mpi/
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):435–458
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: 978-3-540-70940-4
Owen A (2003) The dimension distribution and quadrature test functions. Stat Sin 13:1–17
Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity snalysis in practice: a guide to assessing scientific models. Wiley
Saltelli A, Ratto M, Andres T, Compolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis. The Primer, Wiley
Schmid W, Uhl A (2001) Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Math Comp Sim 55:249–257
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 195–201
SPRNG: scalable parallel random number generator (2010) http://sprng.cs.fsu.edu/
The EGEE-III project website (2010) http://www.eu-egee.org
The SEE-GRID-SCI project website (2010) http://www.see-grid-sci.eu
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by: Can Özturan
This work is partially supported by EC through SEE-GRID-SCI project and by Bulgarian National Science Fund through grant DO02-146.
Rights and permissions
About this article
Cite this article
Atanassov, E., Karaivanova, A., Gurov, T. et al. Quasi-Monte Carlo integration on the grid for sensitivity studies. Earth Sci Inform 3, 289–296 (2010). https://doi.org/10.1007/s12145-010-0069-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-010-0069-9