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Recent Developments in the Theory and Application of the Sparse Grid Combination Technique

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Software for Exascale Computing - SPPEXA 2013-2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 113))

Abstract

Substantial modifications of both the choice of the grids, the combination coefficients, the parallel data structures and the algorithms used for the combination technique lead to numerical methods which are scalable. This is demonstrated by the provision of error and complexity bounds and in performance studies based on a state of the art code for the solution of the gyrokinetic equations of plasma physics. The key ideas for a new fault-tolerant combination technique are mentioned. New algorithms for both initial- and eigenvalue problems have been developed and are shown to have good performance.

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Acknowledgements

The work presented here reviews some results of a German-Australian collaboration going over several years which was supported by grants from the German DFG (SPP-1648 SPPEXA: EXAHD) and the Australian ARC (LP110200410), contributions by Fujitsu Laboratories of Europe (FLE) and involved researchers from the ANU, FLE, TUM, and the Universities of Stuttgart and Bonn. Contributors to this research included Stephen Roberts, Jay Larson, Moshin Ali, Ross Nobes, James Southern, Nick Wilson, Hans-Joachim Bungartz, Valeriy Khakhutskyy, Alfredo Hinojosa, Mario Heene, Michael Griebel, Jochen Garcke, Rico Jacob, Philip Hupp, Yuan Fang, Matthias Wong, Vivien Challis and several others.

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Authors and Affiliations

  1. Mathematical Sciences Institute, The Australian National University, Canberra, Australia

    Markus Hegland & Brendan Harding

  2. Chair of Scientific Computing, Technische Universität München, Munich, Germany

    Christoph Kowitz

  3. Institute for Parallel and Distributed Systems, University of Stuttgart, Stuttgart, Germany

    Dirk Pflüger

  4. Engineering and Computer Science, The Australian National University, Canberra, Australia

    Peter Strazdins

Authors
  1. Markus Hegland
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  2. Brendan Harding
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  3. Christoph Kowitz
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  4. Dirk Pflüger
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  5. Peter Strazdins
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Corresponding author

Correspondence to Markus Hegland .

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Editors and Affiliations

  1. Technische Universität München Institut für Informatik, Garching, Bayern, Germany

    Hans-Joachim Bungartz

  2. Technische Universität München Institut für Informatik, Garching, Germany

    Philipp Neumann

  3. Technische Universität Dresden, Dresden, Germany

    Wolfgang E. Nagel

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Hegland, M., Harding, B., Kowitz, C., Pflüger, D., Strazdins, P. (2016). Recent Developments in the Theory and Application of the Sparse Grid Combination Technique. In: Bungartz, HJ., Neumann, P., Nagel, W. (eds) Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-40528-5_7

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