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Adaptive Parallel Average Schwarz Preconditioner for Crouzeix-Raviart Finite Volume Method

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Parallel Processing and Applied Mathematics (PPAM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13827))

Abstract

In this paper, we describe and analyze an Average Schwarz Method with spectrally enriched coarse space for a Crouzeix-Raviart finite volume element discretization of a multiscale problem. The derived preconditioner is symmetric and we apply GMRES iterative method to the preconditioned problem obtaining the convergence rate of GMRES weakly dependent on the ratio of the coarse to fine mesh h/H if the enrichments of the coarse space contain sufficiently many specially constructed eigenfunctions.

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Authors and Affiliations

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

    Leszek Marcinkowski

  2. Faculty of Engineering and Science, Western Norway University of Applied Sciences, Inndalsveien 28, 5063, Bergen, Norway

    Talal Rahman

Authors
  1. Leszek Marcinkowski
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  2. Talal Rahman
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Correspondence to Leszek Marcinkowski .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  3. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Marcinkowski, L., Rahman, T. (2023). Adaptive Parallel Average Schwarz Preconditioner for Crouzeix-Raviart Finite Volume Method. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2022. Lecture Notes in Computer Science, vol 13827. Springer, Cham. https://doi.org/10.1007/978-3-031-30445-3_25

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  • DOI: https://doi.org/10.1007/978-3-031-30445-3_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-30444-6

  • Online ISBN: 978-3-031-30445-3

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