High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

TL;DR

This paper demonstrates how high-order Discontinuous Galerkin methods can be efficiently implemented on GPUs using Python-based metaprogramming, enhancing computational performance and flexibility.

Contribution

It introduces a novel Python metaprogramming infrastructure tailored for DG methods, facilitating GPU implementation and broadening applicability in computational science.

Findings

DG methods adapt well to GPU architectures

The Python infrastructure simplifies GPU code generation for DG

Significant performance improvements on GPU implementations

Abstract

Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without compromising simulation stability. In a recent publication, we have shown that DG methods also adapt readily to execution on modern, massively parallel graphics processors (GPUs). A number of qualities of the method contribute to this suitability, reaching from locality of reference, through regularity of access patterns, to high arithmetic intensity. In this article, we illuminate a few of the more practical aspects of bringing DG onto a GPU, including the use of a Python-based metaprogramming infrastructure that was created specifically to support DG, but has found many uses across all disciplines of computational science.