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SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation

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Domain Decomposition Methods in Science and Engineering XXIII

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

Abstract

In domain decomposition methods, coarse spaces are traditionally added to make the method scalable. Coarse spaces can however do much more: they can act on other error components that the subdomain iteration has difficulties with, and thus accelerate the overall solution process. We identify here the optimal coarse space for RAS, where optimal does not refer to scalable, but to best possible. This coarse space leads to convergence of the subdomain iterative method in two steps. Since this coarse space is very rich, we propose an approximation which turns out to be also very effective for multiscale problems.

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Author information

Authors and Affiliations

  1. Section of Mathematics, University of Geneva, 1211, Geneva 4, Switzerland

    Martin J. Gander

  2. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    Atle Loneland

Authors
  1. Martin J. Gander
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  2. Atle Loneland
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Corresponding author

Correspondence to Atle Loneland .

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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Gander, M.J., Loneland, A. (2017). SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation. In: Lee, CO., 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_32

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