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Numerical Mathematics and Advanced Applications ENUMATH 2015 pp 521–530Cite as

Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 112)

Abstract

Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The two-level overlapping Schwarz method uses a coarse level based on energy minimizing functions. Linear elastic as well as nonlinear, anisotropic hyperelastic structural models are considered in an FSI problem of a pressure wave in a tube. Using our recent parallel implementation of a two-level overlapping Schwarz preconditioner based on the Trilinos library, the total computation time of our FSI benchmark problem was reduced by more than a factor of two compared to the algebraic one-level overlapping Schwarz method used previously. Finally, also strong scalability for our FSI problem is shown for up to 512 processor cores.

Keywords

  • Coarse Level
  • Arbitrary Lagrangian Eulerian
  • Coarse Space
  • Inexact Newton Method
  • GMRES Iteration

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.

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Acknowledgements

The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN at Jülich Supercomputing Centre (JSC). The authors also gratefully acknowledge the Cray XT6m at Universität Duisburg-Essen and the financial support by the German Science Foundation (DFG), project no. KL2094/3-1 and RH122/4-1.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Alexander Heinlein & Axel Klawonn

  2. Fakultät für Mathematik und Informatik, Institut für Numerische Mathematik und Optimierung, Technische Universität Bergakademie Freiberg, Akademiestr. 6, 09596, Freiberg, Germany

    Oliver Rheinbach

Authors
  1. Alexander Heinlein
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  2. Axel Klawonn
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  3. Oliver Rheinbach
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Corresponding author

Correspondence to Alexander Heinlein .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat Manguoğlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

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© 2016 Springer International Publishing Switzerland

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Heinlein, A., Klawonn, A., Rheinbach, O. (2016). Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_50

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