## 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 language | English (US) |
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Title of host publication | Proc. - 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 |

Pages | 606-610 |

Number of pages | 5 |

DOIs | |

State | Published - Nov 23 2011 |

Event | 14th 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 2011 → Aug 26 2011 |

### Publication series

Name | Proc. - 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 |
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### Other

Other | 14th 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 |
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Country | China |

City | Dalian, Liaoning |

Period | 8/24/11 → 8/26/11 |