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.
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Acknowledgments
AK’s research was partially funded by AFOSR under contract number FA9550-07-1-0422, through the AFOSR/NSSEFF Program Award FA9550-10-1-0180 and also under contract DEFG0288ER25053 by the Department of Energy. TW acknowledges the support of AFOSR under grant number FA9550-05-1-0473 and of the National Science Foundation under grant number DMS 0810187. JSH was partially supported by AFOSR, NSF, and DOE. The opinions expressed are the views of the authors. They do not necessarily reflect the official position of the funding agencies.
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Klöckner, A., Warburton, T., Hesthaven, J.S. (2013). High-Order Discontinuous Galerkin Methods by GPU Metaprogramming. In: Yuen, D., Wang, L., Chi, X., Johnsson, L., Ge, W., Shi, Y. (eds) GPU Solutions to Multi-scale Problems in Science and Engineering. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16405-7_23
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