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.

中文翻译：

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GPU 加速的不连续 Galerkin 方法：3450 亿未知数的 30 倍加速

开发了一种用于在笛卡尔网格上离散化可压缩欧拉方程（无粘性流体动力学的控制方程）的不连续 Galerkin 方法，用于通过 OCCA 使用图形处理单元，OCCA 是一种在多线程硬件架构上实现性能可移植性的统一方法。与使用非 CUDA 感知 MPI 通信的仅 CPU 实现相比，解决方案的时间提高了 30 倍，最多可使用 1,536 个 NVIDIA V100 GPU，并且对于包含 3,450 亿个未知数的问题，显示了多达 6,144 个 NVIDIA V100 GPU 的并行强大可扩展性。进行了 CUDA-Aware MPI 通信与非 GPUDirect 通信的比较，证明在由 32 个 NVIDIA V100 GPU 组成的八个节点上额外提高了 24% 的速度。