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A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

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Advanced Finite Element Methods with Applications (FEM 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 128))

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Abstract

A three-level extension of the GDSW overlapping Schwarz preconditioner in two dimensions is presented, constructed by recursively applying the GDSW preconditioner to the coarse problem. Numerical results, obtained for a parallel implementation using the Trilinos software library, are presented for up to 90,000 cores of the JUQUEEN supercomputer. The superior weak parallel scalability of the three-level method is verified. For large problems and a large number of cores, the three-level method is faster by more than a factor of two, compared to the standard two-level method . The three-level method can also be expected to scale when the classical method will already be out-of-memory.

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Acknowledgements

This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) under grants RH 122/3-2 and KL 2094/4-2.

Also, this work is in part supported under grant RH 122/5-2.

The authors gratefully acknowledge the computing the Gauss Centre for Supercomputing e. V. (www.gauss-centre.eu) for providing computing time on the GCS Supercomputer JUQUEEN BG/Q supercomputer [19] at JSC Jülich. GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayrische Akademie der Wissenschaften).

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Authors and Affiliations

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

    Alexander Heinlein & Axel Klawonn

  2. Institut für Numerische Mathematik und Optimierung, Technische Universität Bergakademie Freiberg, Freiberg, Germany

    Oliver Rheinbach & Friederike Röver

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

Correspondence to Oliver Rheinbach .

Editor information

Editors and Affiliations

  1. Institut für Mathematik & Computergestützte Simulation, Universität der Bundeswehr München, Neubiberg, Germany

    Thomas Apel

  2. Institute for Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

    Ulrich Langer

  3. Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

    Arnd Meyer

  4. Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

    Olaf Steinbach

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Heinlein, A., Klawonn, A., Rheinbach, O., Röver, F. (2019). A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_10

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