Discontinuous Galerkin methods on graphics processing units for nonlinear hyperbolic conservation laws

TL;DR

This paper introduces a GPU-accelerated implementation of the modal discontinuous Galerkin method for solving nonlinear hyperbolic conservation laws in two dimensions, demonstrating high performance and accuracy.

Contribution

It presents a novel CUDA-based implementation of the modal DG method for 2D hyperbolic conservation laws, optimized for GPU architectures.

Findings

Achieves high performance on NVIDIA GTX 580 GPU.

Demonstrates effective solution of Euler equations on unstructured meshes.

Performance comparable to existing linear problem implementations.

Abstract

We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element-local approximations. High performance scientific computing suits GPUs well, as these powerful, massively parallel, cost-effective devices have recently included support for double-precision floating point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation on an NVIDIA GTX 580 device. Profiling of our method reveals performance comparable to an existing nodal DG-GPU implementation for linear problems.