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International Conference on Domain Decomposition Methods

DD 2017: Domain Decomposition Methods in Science and Engineering XXIV pp 373–382Cite as

An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions

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

Abstract

We propose robust coarse spaces for two-level overlapping Schwarz preconditioners, which are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja, Smith, Widlund). The resulting two-level methods with adaptive coarse spaces are robust for second order elliptic problems in two dimensions, even in presence of a highly heterogeneous coefficient function, and reduce to the standard GDSW algorithm if no additional coarse basis functions are used.

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Authors and Affiliations

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

    Alexander Heinlein, Axel Klawonn & Jascha Knepper

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

    Oliver Rheinbach

Authors
  1. Alexander Heinlein
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  2. Axel Klawonn
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  3. Jascha Knepper
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  4. Oliver Rheinbach
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Corresponding authors

Correspondence to Alexander Heinlein , Axel Klawonn , Jascha Knepper or Oliver Rheinbach .

Editor information

Editors and Affiliations

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

    Prof. Petter E. Bjørstad

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

    Prof. Susanne C. Brenner

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

    Prof. Lawrence Halpern

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

    Prof. Hyea Hyun Kim

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

    Prof. Dr. Ralf Kornhuber

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

    Prof. Talal Rahman

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

    Prof. Olof B. Widlund

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Heinlein, A., Klawonn, A., Knepper, J., Rheinbach, O. (2018). An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions. In: , 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_35

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