GPU-Accelerated Discontinuous Galerkin Methods: 30x Speedup on 345 Billion Unknowns

A discontinuous Galerkin method for the discretization of the compressible Euler equations, the governing equations of inviscid fluid dynamics, on Cartesian meshes is developed for use of Graphical Processing Units via OCCA, a unified approach to performance portability on multi-threaded hardware architectures. A 30x time-to-solution speedup over CPU-only implementations using non-CUDA-Aware MPI communications is demonstrated up to 1,536 NVIDIA V100 GPUs and parallel strong scalability is shown up to 6,144 NVIDIA V100 GPUs for a problem containing 345 billion unknowns. A comparison of CUDA-Aware MPI communication to non-GPUDirect communication is performed demonstrating an additional 24 % speedup on eight nodes composed of 32 NVIDIA V100 GPUs.