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Numerical Computations with GPUs pp 183–206Cite as

Finite and Spectral Element Methods on Unstructured Grids for Flow and Wave Propagation Problems

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Abstract

Finite element methods are one of the most prominent discretisation techniques for the solution of partial differential equations. They provide high geometric flexibility, accuracy and robustness, and a rich body of theory exists. In this chapter, we summarise the main principles of Galerkin finite element methods, and identify and discuss avenues for their parallelisation. We develop guidelines that lead to efficient implementations, however, we prefer generic ideas and principles over utmost performance tuning.

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Acknowledgements

This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA), through DFG SFB 708 “3D Surface Engineering of Tools for the Sheet Metal Forming—Manufacturing, Modelling, Machining—”, by the European “Mont-Blanc: European scalable and power efficient HPC platform based on low-power embedded technology” #288777 project of call FP7-ICT-2011-7, and by the G8 and French ANR “Interdisciplinary Program on Application Software towards Exascale Computing for Global Scale Issues” (SEISMIC IMAGING project, ANR-10-G8EX-002). This work was granted access to the high-performance computing resources of the French supercomputing centre CCRT under allocation #2012-046351 awarded by GENCI (Grand Equipement National de Calcul Intensif).

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Authors and Affiliations

  1. Department of Mathematics, Institute of Applied Mathematics, TU Dortmund, Dortmund, Germany

    Dominik Göddeke

  2. Laboratory of Mechanics and Acoustics, CNRS UPR 7051, Aix-Marseille University, Centrale Marseille, France

    Dimitri Komatitsch

  3. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Matthias Möller

Authors
  1. Dominik Göddeke
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  2. Dimitri Komatitsch
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  3. Matthias Möller
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Correspondence to Dominik Göddeke .

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Editors and Affiliations

  1. National Center for Supercomputing Applications, University of Illinois, Urbana, Illinois, USA

    Volodymyr Kindratenko

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Göddeke, D., Komatitsch, D., Möller, M. (2014). Finite and Spectral Element Methods on Unstructured Grids for Flow and Wave Propagation Problems. In: Kindratenko, V. (eds) Numerical Computations with GPUs. Springer, Cham. https://doi.org/10.1007/978-3-319-06548-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-06548-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06547-2

  • Online ISBN: 978-3-319-06548-9

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