Paper Info
Title
The Role of Floating Point Precision in Two- and Three-Dimensional High Rayleigh Bénard Convection Modeled on Fermi GPU
Abstract
We have implemented a second-order finite difference method for two-dimensional and three-dimensional Rayleigh-Benard 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 singleand 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.
Year
DOI
Venue
2011
10.1109/CSE.2011.122
Computational Science and Engineering
Keywords
Field
DocType
Benard convection,C language,Earth mantle,Gaussian noise,computer graphic equipment,convergence of numerical methods,coprocessors,finite difference methods,floating point arithmetic,geophysical techniques,geophysics computing,iterative methods,CUBLAS routines,CUDA,Earth mantle convection,Fermi GPU,Gaussian noise,Nusselt number,computational mesh,floating point precision,iterative methods,second-order finite difference method,three-dimensional high Rayleigh Bénard convection,two-dimensional high Rayleigh Bénard convection,word length
Fermi Gamma-ray Space Telescope,Mathematical optimization,Mathematical analysis,Computer science,Floating point,Iterative method,Rayleigh–Bénard convection,Finite difference method,Coprocessor,Gaussian noise,Distributed computing
Conference
ISBN
Citations 
PageRank 
978-1-4577-0974-6
0
0.34
References 
Authors
1
4
Name
Order
Citations
PageRank
David A. Sanchez100.34
David A. Yuen28214.75
Yu-jun Sun300.68
Grady B. Wright425820.84