GPU Accelerated Spectral Element Methods: 3D Euler equations
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A GPU accelerated nodal discontinuous Galerkin method for the solution of the 3D Euler equations in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) is presented. We use algorithms suitable for the single instruction multiple thread architecture of GPUs to accelerate the dynamical core of 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 benchmark problems representative of different scales of atmospheric dynamics.