A GPU Accelerated Continuous and Discontinuous Galerkin Non-hydrostatic Atmospheric Model

Daniel S. Abdi, Lucas C. Wilcox, Timothy Warburton, Francis X. Giraldo
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA
Naval Postgraduate School, 2016


   title={A GPU Accelerated Continuous and Discontinuous Galerkin Non-hydrostatic Atmospheric Model},

   author={Abdia, Daniel S and Wilcoxa, Lucas C and Warburtonb, Timothy and Giraldoa, Francis X},



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We present a GPU accelerated nodal discontinuous Galerkin method for the solution of the three dimensional Euler equations, which are nonlinear hyperbolic equations that govern the motion and thermodynamic state of the atmosphere. The part of the solution process that solves the governing equations of motion with no moist processes is called the dynamical core. Acceleration of this dynamical core plays an important practical role in not only getting daily forecasts faster but also in obtaining more accurate (high resolution) results within a given simulation time limit. We use algorithms suitable for the single instruction multiple thread architecture of GPUs to accelerate NUMA by two orders of magnitude relative to one core of a CPU. Tests on one node of the Titan supercomputer yield a speedup of upto 15X on one K20x GPU relative to that on an AMD Opteron CPU with 16 cores. The scalability of the multi-GPU implementation is tested using 16384 GPUs, which resulted in a weak scaling efficiency of about 90%. For portability to heterogeneous computing environment, we used a new programming language OCCA, which can be cross-compiled to either OpenCL, CUDA or OpenMP at runtime. Finally, the accuracy and performance of our GPU implementations are verified using several benchmark problems representative of different scales of atmospheric dynamics.
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