Impact of Floating-Point Precision on Boundary Layer Instabilities Modeled on Fermi GPU

David A. Sanchez, David A. Yuen, Yujun Sun, Grady B. Wright
Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455, U.S.A.
University of Minnesota, Supercomputing Institute, Research Report UMSI 2011/32, 2011


   title={Impact of Floating-Point Precision on Boundary Layer Instabilities Modeled on Fermi GPU},

   author={Sanchez, D.A. and Yuen, D.A. and Sun, Y. and Wright, G.B.},



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We have implemented two-dimensional and three-dimensional Rayleigh-Benard convection for infinite Prandtl number, appropriate for the Earth’s mantle, on a single Fermi GPU by utilizing a second-order finite-difference method. The code was written in C for CUDA and heavily itilized optimized CUBLAS routines. These implementations enjoyed performance on the order 535 GFLOP/s and 100 GFLOP/s in single(32-bit)-precision and 230 GFLOP/s and 70 GFLOP/s in double(64-bit)-precision on Fermi GPU. Acknowledging the sinsivity of this model, we explore the suitability of single-precision for this simulation, finding that global characteristics of the model remain intact despite the loss of precision. These findings indicate that problems found in implementing the code in double-precision on GPU could be investigated in single-precision, saving not only computing time, but money and power-consumption as well. This is of particular interest in studying the mantle convection paradigm, as higher Rayleigh numbers, appropriate for the young Earth, imply higher mantle convective velocities. These velocities necessitate a smaller mesh and shorter (non-dimensionalized) timestamp to properly resolve the fine-scale dynamically evolving features.
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