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Scientific Computing Group Report - Detail view

Identifier: 2008-27

Author(s): A. Kloeckner, T. Warburton, J. Bridge, and J.S. Hesthaven

Title: Nodal Discontinuous Galerkin Methods on Graphics Processors

Page count: 33 pp.

Date: Dec. 18, 2008


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 ma jority 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 repre- sented 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 40 to 60 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.


  title = "{Nodal Discontinuous Galerkin Methods on Graphics Processors}",
  author = "A. Kloeckner, T. Warburton, J. Bridge, and J.S. Hesthaven",
  institution = "Scientific Computing Group, Brown University",
  number = "2008-27",
  address = "Providence, RI, USA",
  year = 2008,
  month = dec,