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Two New Enriched Multiscale Coarse Spaces for the Additive Average Schwarz Method

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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 this paper we introduce an Average Additive Schwarz method with spectrally enriched coarse grids for a standard Finite Element discretization of a second order elliptic problem with discontinuous coefficients, where the discontinuities are inside subdomains and across subdomain boundaries. The proposed methods depend linearly on the mesh parameters H∕h, i.e., depending on the distribution of the coefficient in the model problem, the parameters describing the convergence of the PCG method used to solve the preconditioned system depends linearly or on the mesh parameters. 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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Acknowledgements

Leszek Marcinkowski was partially supported by Polish Scientific Project no 2016/21/B/ST1/00350.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Leszek Marcinkowski

  2. Faculty of Engineering, Bergen University College, Inndalsveien 28, 5063, Bergen, Norway

    Talal Rahman

Authors
  1. Leszek Marcinkowski
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  2. Talal Rahman
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Corresponding author

Correspondence to Leszek Marcinkowski .

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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Marcinkowski, L., Rahman, T. (2017). Two New Enriched Multiscale Coarse Spaces for the Additive Average Schwarz Method. 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_40

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