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Numerical integration on GPUs for higher order finite elements

Krzysztof Banas, Przemyslaw Plaszewski, Pawel Maciol
Department of Applied Computer Science and Modelling, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krakow, Poland
arXiv:1310.1191 [cs.MS], (4 Oct 2013)

@article{2013arXiv1310.1191B,

   author={Bana{‘s}}, K. and {P{l}aszewski}, P. and {Macio{l}}, P.},

   title={"{Numerical integration on GPUs for higher order finite elements}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1310.1191},

   primaryClass={"cs.MS"},

   keywords={Computer Science – Mathematical Software},

   year={2013},

   month={oct},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1310.1191B},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose integration procedures, as well as particular example applications. The most important characteristic of the problem investigated is the large variation of required processor and memory resources associated with different degrees of approximating polynomials. The questions that we try to answer are whether it is possible to design a single integration kernel for different GPUs and different orders of approximation and what performance can be expected in such a case.
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