The role of floating point precision in two- and three-dimensional high Rayleigh Bénard convection modeled on Fermi GPU

David A. Sanchez, David A. Yuen, Yujun Sun, Grady B. Wright

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We have implemented a second-order finite difference method for two-dimensional and three-dimensional Rayleigh-Béanard thermal convection, corresponding to convection in the Earth's mantle, on a single Fermi GPU. These codes are written in C for CUDA, making heavy use of CUBLAS routines for efficiency, and achieve performance on the order of 535 GFLOP/s and 100 GFLOP/s in single-precision and 230 GLFOP/s and 70 GFLOP/s in double-precision. We explore the sensitivity of this model to word length, finding that global characteristics remain constant despite a change in precision. Specifically, we compare the divergence between single- and double-precision runs with exactly identical initial conditions to the divergence between double-precision runs whose initial conditions have been perturbed by Gaussian noise. Our finding is that large-scale quantitative behavior (Nusselt number, number of plumes, etc) does not vary among these samples. This observation suggests a saving in time and computing resources could be enjoyed by implementing certain problems in single-precision. This is also valuable to scientists using iterative methods, as convergence may be completely unaffected by change of precision before the last few iterations. A particular interest is developed in the context of young Earth mantle convection, where higher Rayleigh numbers require both a finer computational mesh and a shorter timestep to properly resolve dynamic, small-scale features - compounding time wasted by inefficient or overly conservative computational implementations.

Original languageEnglish (US)
Title of host publicationProc. - 14th IEEE Int. Conf. on Computational Science and Engineering, CSE 2011 and 11th Int. Symp.on Pervasive Systems, Algorithms, and Networks, I-SPAN 2011 and 10th IEEE Int. Conf. IUCC 2011
Pages606-610
Number of pages5
DOIs
StatePublished - Nov 23 2011
Event14th IEEE Int. Conf. on Computational Science and Engineering, CSE 2011, the 11th International Symposium on Pervasive Systems, Algorithms, and Networks, I-SPAN 2011, and the 10th IEEE Int. Conf. on Ubiquitous Computing and Communications, IUCC 2011 - Dalian, Liaoning, China
Duration: Aug 24 2011Aug 26 2011

Publication series

NameProc. - 14th IEEE Int. Conf. on Computational Science and Engineering, CSE 2011 and 11th Int. Symp. on Pervasive Systems, Algorithms, and Networks, I-SPA 2011 and 10th IEEE Int. Conf. on IUCC 2011

Other

Other14th IEEE Int. Conf. on Computational Science and Engineering, CSE 2011, the 11th International Symposium on Pervasive Systems, Algorithms, and Networks, I-SPAN 2011, and the 10th IEEE Int. Conf. on Ubiquitous Computing and Communications, IUCC 2011
CountryChina
CityDalian, Liaoning
Period8/24/118/26/11

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