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Domain Decomposition Methods in Science and Engineering XXIII pp 353–360Cite as

Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 116)

Abstract

Parallel results obtained with a new implementation of an overlapping Schwarz method using an energy minimizing coarse space are presented. We consider structured and unstructured domain decompositions for scalar elliptic and linear elasticity model problems in two dimensions. In particular, strong and weak parallel scalability studies for up to 1024 processor cores are presented for both types of problems. Additionally, weak scalability results for a three-dimensional linear elasticity model problem using up to 4096 processor cores are discussed. Finally, an application from fully-coupled fluid-structure interaction using a nonlinear hyperelastic material model for the structure is shown.

Keywords

  • Model Problem
  • Linear Elasticity
  • Processor Core
  • Weak Scalability
  • Schwarz Method

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 acknowledge the use of the JUQUEEN BG/Q supercomputer (Stephan and Docter, 2015) at JSC Jülich, the use of the Cray XT6m at Universität Duisburg-Essen and the financial support by the German Science Foundation (DFG), project no. KL2094/3 and RH122/4.

Author information

Authors and Affiliations

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

    Alexander Heinlein & Axel Klawonn

  2. Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und Informatik, 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. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Heinlein, A., Klawonn, A., Rheinbach, O. (2017). Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space. In: , et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_36

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