GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms

TL;DR

This paper presents an GPU implementation of an entropy-stable discontinuous Galerkin solver for Euler equations, demonstrating high performance, scalability, and energy efficiency on NVIDIA A100 hardware.

Contribution

The paper introduces a GPU-optimized entropy-stable DG solver for Euler equations with non-conservative terms, achieving significant speedup and efficiency improvements.

Findings

GPU solver reaches 70% of peak performance on A100 hardware.

GPU kernels are 10x faster and 13x more energy-efficient than CPU code.

Solver achieves 2x speedup at 32-bit precision.

Abstract

The entropy-stable discontinuous Galerkin method for compressible Euler equations with buoyancy is implemented on graphics processing unit (GPU) hardware. We measure the performance of the solver on three-dimensional problems: the rising thermal bubble and the baroclinic instability in a channel. On NVIDIA A100 hardware, the solver achieves nearly 70\% of 64-bit floating-point peak performance for the most computationally expensive kernel (volume terms) and significantly reduces the computational overhead typically incurred by two point entropy-stable fluxes in the volume terms. We also present impressive strong and weak scaling performance of the solver and compare to a highly-optimized central processing unit (CPU) code showing that the GPU kernels are a factor of $10\times$ faster and better than $13\times$ more energy efficient than the CPU code. We also show that the solver achieves the expected $2\times$ speedup when run at 32-bit floating-point peak performance. We discuss the different modifications that we implemented to reach the final form of the GPU implementation and measure the performance gain of each of the implementation strategies ranging from reduction in complex operations and memory traffic as well as load balancing. We also extend symmetry-based flux savings to the non-symmetric gravity term, preserving nearly the full factor-of-two speedup achieved for the symmetric flux.