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Inexact Spectral Deferred Corrections

  • Robert SpeckEmail author
  • Daniel Ruprecht
  • Michael Minion
  • Matthew Emmett
  • Rolf Krause
Part of the Lecture Notes in Computational Science and Engineering book series (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.

Keywords

Stiff Problem Multigrid Solver Euler Step Viscous Burger Spectral Deferred Correction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Robert Speck
    • 1
    • 2
    Email author
  • Daniel Ruprecht
    • 2
  • Michael Minion
    • 3
  • Matthew Emmett
    • 4
  • Rolf Krause
    • 2
  1. 1.Jülich Supercomputing Centre, Forschungszentrum Jülich GmbHJülichGermany
  2. 2.Institute of Computational ScienceUniversità della Svizzera italianaLuganoSwitzerland
  3. 3.Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  4. 4.Center for Computational Sciences and EngineeringLawrence Berkeley National LaboratoryBerkeleyUSA

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