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International Conference on Domain Decomposition Methods

DD 2017: Domain Decomposition Methods in Science and Engineering XXIV pp 129–137Cite as

Does SHEM for Additive Schwarz Work Better than Predicted by Its Condition Number Estimate?

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

Abstract

The SHEM (Spectral Harmonically Enriched Multiscale) coarse space is a new coarse space for arbitrary overlapping or non-overlapping domain decomposition methods.

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Notes

  1. 1.

    Any other Sturm Liuville problem could be used as well to get a different variant of SHEM, for example more expensive Schur complements corresponding to the Dirichlet to Neumann maps [11], or one could construct even cheaper interface basis functions without eigenvalue problem, see [8].

References

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Author information

Authors and Affiliations

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

    Petter E. Bjørstad & Atle Loneland

  2. Section of Mathematics, University of Geneva, Geneva, Switzerland

    Martin J. Gander

  3. Department of Computing, Mathematics and Physics, Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

Authors
  1. Petter E. Bjørstad
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  2. Martin J. Gander
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  3. Atle Loneland
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  4. Talal Rahman
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Corresponding authors

Correspondence to Petter E. Bjørstad , Martin J. Gander , Atle Loneland or Talal Rahman .

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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Bjørstad, P.E., Gander, M.J., Loneland, A., Rahman, T. (2018). Does SHEM for Additive Schwarz Work Better than Predicted by Its Condition Number Estimate?. 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_10

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