Nodal discontinuous Galerkin methods on graphics processors

By Andreas Klöckner, Tim Warburton, Jeff Bridge, Jan S. Hesthaven. Journal of Computational Physics, 2009

415 citations recorded by the source corpus.

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. Lately, another property of DG has been growing in importance: The majority of a DG operator is applied in an element-local way, with weak penalty-based element-to-element coupling. The resulting locality in memory access is one of the factors that enables DG to run on off-the-shelf, massively parallel graphics processors (GPUs). In addition, DG's high-order nature lets it require fewer data points per represented wavelength and hence fewer memory accesses, in exchange for higher arithmetic intensity. Both of these factors work significantly in favor of a GPU implementation of DG. Using a single US$400 Nvidia GTX 280 GPU, we accelerate a solver for Maxwell's equations on a general 3D unstructured grid by a factor of around 50 relative to a serial computation on a current-generation CPU. In many cases, our algorithms exhibit full use of the device's available memory bandwidth. Example computations achieve and surpass 200gigaflops/s of net application-level floating point work. In this article, we describe and derive the techniques used to reach this level of performance. In addition, we present comprehensive data on the accuracy and runtime behavior of the method.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/852e427df0329c0b9b033783246c3189b65b0a04

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Citations in the corpus

An analysis of the spectrum of the discontinuous Galerkin method (2013, methodology): “In recent years, the DGM has been used with a variety of explicit time integrat ion schemes, such as AdamsBashforth [8], strong-stability preserving schemes [9], l ow storage RK schemes [13].”
High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster (2010, methodology): “[47] implemented a discontinuous Galerkin technique to solve Maxwell’s equations on a single GPU and propagate electromagnetic waves.”
PyCUDA and PyOpenCL: A scripting-based approach to GPU run-time code generation (2009, background): “A number of techniques for dealing with this problem are enumerated and evaluated in [23].”
Discontinuous Galerkin methods in nanophotonics (2011, background): “For this reason, DGTD is an ideal candidate for parallelisation on multiple cores, computers, and graphics cards [63].”