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Robust Solutions to PDEs with Multiple Grids

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Sparse Grids and Applications - Munich 2012

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 97))

Abstract

In this paper we will discuss some approaches to fault-tolerance for solving partial differential equations. In particular we will discuss how one can combine the solution from multiple grids using ideas related to the sparse grid combination technique and multivariate extrapolation. By utilising the redundancy between the solutions on different grids we will demonstrate how this approach can be adapted for fault-tolerance. Much of this will be achieved by assuming error expansions and examining the extrapolation of these when various solutions from different grids are combined.

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Acknowledgements

This research was supported under the Australian Research Council’s Linkage Projects funding scheme (project number LP110200410). We are grateful to Fujitsu Laboratories of Europe for providing funding as the collaborative partner in this project.

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Authors and Affiliations

  1. Australian National University, Canberra, ACT, 0200, Australia

    Brendan Harding & Markus Hegland

Authors
  1. Brendan Harding
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  2. Markus Hegland
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Corresponding author

Correspondence to Brendan Harding .

Editor information

Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  2. Institute for Parallel and Distributed Systems, Universität Stuttgart, Stuttgart, Germany

    Dirk Pflüger

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Harding, B., Hegland, M. (2014). Robust Solutions to PDEs with Multiple Grids. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Munich 2012. Lecture Notes in Computational Science and Engineering, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-04537-5_7

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