×

Simulation of stochastic processes using graphics hardware. (English) Zbl 1221.65025

Summary: Graphics Processing Units (GPUs) were originally designed to manipulate images, but due to their intrinsic parallel nature, they turned into a powerful tool for scientific applications. In this article, we evaluated GPU performance in an implementation of a traditional stochastic simulation – the correlated Brownian motion. This movement can be described by the generalized Langevin equation, which is a stochastic integro-differential equation, with applications in many areas like anomalous diffusion, transport in porous media, noise analysis, quantum dynamics, among many others. Our results show the power inherent in GPU programming when compared to traditional CPUs (Intel): we observed acceleration values up to sixty times by using a NVIDIA GPU in place of a single-core Intel CPU.

MSC:

65C50 Other computational problems in probability (MSC2010)

Software:

CUDA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lee, M. H., J. Math. Phys., 24, 2512 (1983)
[2] Kubo, R., Rep. Prog. Phys., 29, 255 (1966)
[3] L. Weiss, W. Mathis, IEEE International Symposium on Circuits and Systems, Hong Kong, June 9-12, 1997.; L. Weiss, W. Mathis, IEEE International Symposium on Circuits and Systems, Hong Kong, June 9-12, 1997.
[4] Morgado, R.; Oliveira, F. A.; Batrouni, G. G.; Hansen, A., Phys. Rev. Lett., 89, 100601 (2002)
[5] Roy, S.; Mitra, I.; Llinas, R., Phys. Rev. E, 78, 041920 (2008)
[6] Bouchaud, J.-P.; Cont, R., Eur. Phys. J. B, 6, 543-550 (1998)
[7] I. Buck, Brook Language Specification 0.2, in: http://merrimac.stanford.edu/brook; I. Buck, Brook Language Specification 0.2, in: http://merrimac.stanford.edu/brook
[8] NVIDIA Corporation, NVIDIA CUDA Compute Unified Device Architecture Programming Guide, Version 2.0, 2008.; NVIDIA Corporation, NVIDIA CUDA Compute Unified Device Architecture Programming Guide, Version 2.0, 2008.
[9] Matsumoto, M.; Nishimura, T., ACM Trans. on Modeling and Computer Simulation, 8, 1, 3-30 (January 1998)
[10] Moore, S. K., Spectrum IEEE, 45, 11, 15 (November 2008)
[11] Lapas, L. C.; Morgado, R.; Vainstein, M. H.; Rubi, J. M.; Oliveira, F. A., Phys. Rev. Lett., 101, 230602 (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.