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Using Algebraic Multigrid in Inexact BDDC Domain Decomposition Methods

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

A highly scalable implementation of an inexact BDDC (Balancing Domain Decomposition by Constraints) method is presented, and scalability results for linear elasticity problems in two and three dimensions for up to 131,072 computational cores of the JUQUEEN BG/Q are shown. In this method, the inverse action of the partially coupled stiffness matrix is replaced by V-cycles of an AMG (algebraic multigrid) method. The use of classical AMG for systems of PDEs, based on a nodal coarsening approach is compared with a recent AMG method using an explicit interpolation of the rigid body motions (global matrix approach; GM). It is illustrated, that for systems of PDEs an appropriate AMG interpolation is mandatory for fast convergence, i.e., using exact interpolation of rigid body modes in elasticity.

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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 KL 2094/4-1, KL 2094/4-2, RH 122/2-1, and RH 122/3-2. The authors also gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de) and JUQUEEN [11] at Jülich Supercomputing Centre (JSC, www.fz-juelich.de/ias/jsc). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).

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Authors and Affiliations

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

    Axel Klawonn & Martin Lanser

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

    Oliver Rheinbach

Authors
  1. Axel Klawonn
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  2. Martin Lanser
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  3. Oliver Rheinbach
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Corresponding authors

Correspondence to Axel Klawonn , Martin Lanser or Oliver Rheinbach .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

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

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

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

    Olof B. Widlund

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Klawonn, A., Lanser, M., Rheinbach, O. (2018). Using Algebraic Multigrid in Inexact BDDC Domain Decomposition Methods. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_40

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