Nodal discontinuous Galerkin methods on graphics processors

A. Klöckner, T. Warburton, J. Bridge, J. S. Hesthaven

Research output: Contribution to journalArticlepeer-review


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 200 gigaflops/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.

Original languageEnglish (US)
Pages (from-to)7863-7882
Number of pages20
JournalJournal of Computational Physics
Issue number21
StatePublished - Nov 20 2009
Externally publishedYes


  • Discontinuous Galerkin
  • GPU
  • High order
  • Many-core
  • Maxwell's equations
  • Parallel computation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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