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Schwarz Preconditioner with Face Based Coarse Space for Multiscale Elliptic Problems in 3D

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Parallel Processing and Applied Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9574))

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Abstract

We present a parallel preconditioner based on the domain decomposition for the finite element discretization of multiscale elliptic problems in 3D with highly heterogeneous coefficients. The proposed preconditioner is constructed using an abstract framework of the Additive Schwarz Method which is intrinsically parallel. The coarse space consists of multiscale finite element functions associated with the wire basket, and is enriched with functions based on solving carefully constructed generalized eigen value problem locally on each face. The convergence rate of the Preconditioned Conjugate Method with the proposed preconditioner is shown to be independent of the variations in the coefficients for sufficient number of eigenfunctions in the coarse space.

L. Marcinkowski—This work was partially supported by Polish Scientific Grant 2011/01/B/ST1/01179 and Chinese Academy of Science Project: 2013FFGA0009 - GJHS20140901004635677.

T. Rahman—The author acknowledges the support of NRC through the DAADppp project 233989.

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Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Leszek Marcinkowski

  2. Department of Computing, Mathematics and Physics, 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. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Marcinkowski, L., Rahman, T. (2016). Schwarz Preconditioner with Face Based Coarse Space for Multiscale Elliptic Problems in 3D. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_32

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  • DOI: https://doi.org/10.1007/978-3-319-32152-3_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32151-6

  • Online ISBN: 978-3-319-32152-3

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