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High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

Andreas Klockner, Timothy Warburton, Jan S. Hesthaven
Courant Institute of Mathematical Sciences, New York University, New York, NY
Scientific Computing Group, Division of Applied Mathematics, Brown University, Tech. report 2011-13

@techreport{brown_sc_2011_13,

   title={High-Order Discontinuous Galerkin Methods by GPU Metaprogramming},

   author={A. Kloeckner, T. Warburton and J. S. Hesthaven},

   institution={"ScientificComputingGroup},

   number={"2011-13"},

   address={"Providence},

   year={2011},

   month={jun}

}

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Discontinuous Galerkin (DG) methods for the numerical solution of par- tial 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.
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