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International Conference on Domain Decomposition Methods

DD 2017: Domain Decomposition Methods in Science and Engineering XXIV pp 475–482Cite as

Additive Schwarz with Vertex Based Adaptive Coarse Space for Multiscale Problems in 3D

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

Abstract

In this paper an overlapping additive Schwarz method with a spectrally enriched coarse space is proposed. The method is for solving the standard Finite Element discretization of second order elliptic problems in there dimensions with discontinuous coefficients, where the discontinuities are inside subdomains and across subdomain boundaries. In case when the coarse space is large enough the convergence of the PCG method is independent of jumps in the coefficient.

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Acknowledgment

The work of “L. Marcinkowski” was partially supported by Polish Scientific Grant 2016/21/B/ST1/00350.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Warsaw, Warszawa, Poland

    Leszek Marcinkowski

  2. Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

Authors
  1. Leszek Marcinkowski
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  2. Talal Rahman
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Corresponding authors

Correspondence to Leszek Marcinkowski 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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Marcinkowski, L., Rahman, T. (2018). Additive Schwarz with Vertex Based Adaptive Coarse Space for Multiscale Problems in 3D. 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_45

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