Solving Wave Equations on Unstructured Geometries

TL;DR

This paper presents a GPU-accelerated discontinuous Galerkin method for solving wave equations on unstructured geometries, achieving high accuracy and real-time visualization with a compact implementation.

Contribution

It provides an accessible implementation of a GPU-based DG wave solver, demonstrating high accuracy and real-time performance on complex geometries.

Findings

Achieves high accuracy with DG methods on GPUs

Enables real-time wave visualization

Provides a compact, 1500-line implementation

Abstract

Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational study of waves meets a trade-off of two figures of merit--its computational speed and its accuracy. Discontinuous Galerkin (DG) methods fall on the high-accuracy end of this spectrum. Fortuitously, their computational structure is so ideally suited to GPUs that they also achieve very high computational speeds. In other words, the use of DG methods on GPUs significantly lowers the cost of obtaining accurate solutions. This article aims to give the reader an easy on-ramp to the use of this technology, based on a sample implementation which demonstrates a highly accurate, GPU-capable, real-time visualizing finite element solver in about 1500 lines of code.