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Inexact Spectral Deferred Corrections

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Domain Decomposition Methods in Science and Engineering XXII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 104))

Abstract

Implicit integration methods based on collocation are attractive for a number of reasons, e.g. their ideal (for Gauss-Legendre nodes) or near ideal (Gauss-Radau or Gauss-Lobatto nodes) order and stability properties. However, straightforward application of a collocation formula with M nodes to an initial value problem with dimension d requires the solution of one large Md × Md system of nonlinear equations.

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Acknowledgement

This work was supported by the Swiss National Science Foundation (SNSF) under the lead agency agreement through the project “ExaSolvers” within the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) of the Deutsche Forschungsgemeinschaft (DFG). Matthew Emmett and Michael Minion were supported by the Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the U.S. Department of Energy under contract DE-AC02-05CH11231. Michael Minion was also supported by the U.S. National Science Foundation grant DMS-1217080. The authors acknowledge support from Matthias Bolten, who provided the employed multigrid solver.

Author information

Authors and Affiliations

  1. Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany

    Robert Speck

  2. Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland

    Robert Speck, Daniel Ruprecht & Rolf Krause

  3. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA

    Michael Minion

  4. Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Matthew Emmett

Authors
  1. Robert Speck
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  2. Daniel Ruprecht
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  3. Michael Minion
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  4. Matthew Emmett
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  5. Rolf Krause
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Corresponding author

Correspondence to Robert Speck .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Garching, Germany

    Thomas Dickopf

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Geométrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. Institute of Computational Science, University of Lugano, Lugano, Switzerland

    Rolf Krause

  5. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Luca F. Pavarino

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Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R. (2016). Inexact Spectral Deferred Corrections. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_39

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