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High Rayleigh Number Mantle Convection on GPU

David A. Sanchez, Christopher Gonzalez, David A. Yuen, Grady B. Wright, Gregory A. Barnett
Supercomputing Institute Research Report, University of Minnesota
University of Minnesota, Supercomputing Institute Research Report, UMSI 2011/28, 2011

@article{sanchez2011high,

   title={High Rayleigh Number Mantle Convection on GPU},

   author={Sanchez, D. and Gonzalez, C. and Yuen, D. and Wright, G. and Barnett, G.},

   journal={Yuen, D., Wang, J., Johnsson, L., Chi, C., Shi, Y., GPU Solutions to Multi-Scale Problems in Science and Engineering, Springer},

   year={2011}

}

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We implemented two- and three-dimensional Rayleigh-Benard convection on Nvidia GPUs by utilizing a 2nd-order finite difference method. By exploiting the massive parallelism of GPU using both CUDA for C and optimized CUBLAS routines, we have on a single Fermi GPU run simultaneous of Raileigh number up to 6×10^10 (on a mesh of 2000×4000 uniform grid points) in two dimensions and up to 10^7 (on a mesh of 450x450x225 uniform grid points) for three dimensions. On Nvidia Tesla C2070 GPUs, these implementations enjoy single-precision performance of 535 GFLOP/s and 100 GFLOP/s respectively, and double-precision performance of 230 GFLOP/s and 70 GFLOP/s respectively.
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