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

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.

[1]  Alejandro Duran,et al.  Productive Programming of GPU Clusters with OmpSs , 2012, 2012 IEEE 26th International Parallel and Distributed Processing Symposium.

[2]  Peter S. Pacheco.  Parallel programming with MPI , 1996 .

[3]  Michael Mascagni,et al.  SPRNG: A Scalable Library for Pseudorandom Number Generation , 1999, PP.

[4]  J. Mark Bull,et al.  Parallel globally adaptive quadrature on the KSR-1 , 1994, Adv. Comput. Math..

[5]  Massimiliano Fatica.  Accelerating linpack with CUDA on heterogenous clusters , 2009, GPGPU-2.

[6]  Alan M. Ferrenberg,et al.  Monte Carlo simulations: Hidden errors from "good" random number generators. , 1992, Physical review letters.

[7]  Hongmei Chi,et al.  Parallel linear congruential generators with Sophie-Germain moduli , 2004, Parallel Comput..

[8]  Przemyslaw Stpiczynski.  Solving linear recurrences on hybrid GPU accelerated manycore systems , 2011, 2011 Federated Conference on Computer Science and Information Systems (FedCSIS).

[9]  Thomas Hahn,et al.  Cuba - a library for multidimensional numerical integration , 2004, Comput. Phys. Commun..

[10]  Przemyslaw Stpiczynski,et al.  Parallel GPU-accelerated recursion-based generators of pseudorandom numbers , 2012, 2012 Federated Conference on Computer Science and Information Systems (FedCSIS).

[11]  John E. Stone,et al.  GPU clusters for high-performance computing , 2009, 2009 IEEE International Conference on Cluster Computing and Workshops.

[12]  H. Niederreiter.  Quasi-Monte Carlo methods and pseudo-random numbers , 1978 .

[13]  Michael Mascagni.  Parallel Linear Congruential Generators with Prime Moduli , 1998, Parallel Comput..

[14]  Michael Mascagni,et al.  Testing parallel random number generators , 2003, Parallel Comput..

[15]  Michael Mascagni,et al.  Parameterizing parallel multiplicative lagged-Fibonacci generators , 2004, Parallel Comput..

[16]  Michael Mascagni,et al.  Corrigendum: Algorithm 806: SPRNG: a scalable library for pseudorandom number generation , 2000, TOMS.

[17]  Robert Strzodka,et al.  Exploring weak scalability for FEM calculations on a GPU-enhanced cluster , 2007, Parallel Comput..