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Additive Average Schwarz with Adaptive Coarse Space for Morley FE

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Parallel Processing and Applied Mathematics (PPAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12044))

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Abstract

We propose an additive average Schwarz preconditioner with two adaptively enriched coarse space for the nonconforming Morley finite element method for fourth order biharmonic equation with highly varying and discontinuous coefficients. In this paper, we extend the work of [9, 10]: (additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems). Our analysis shows that the condition number of the preconditioned problem is bounded independent of the jump of the coefficient, and it depends only on the ratio of the coarse to the fine mesh.

The work of the last author was partially supported by Polish Scientific Grant: National Science Center 2016/21/B/ST1/00350.

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Acknowledgments

The authors are deeply thankful for Prof. Talal Rahman for his invaluable comments, discussions, and suggestions in this work.

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Authors and Affiliations

  1. Department of Computing, Mathematics, and Physics, Western Norway University of Applied Sciences, Inndalsveien 28, 5020, Bergen, Norway

    Salah Alrabeei & Mahmood Jokar

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

    Leszek Marcinkowski

Authors
  1. Salah Alrabeei
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  2. Mahmood Jokar
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  3. Leszek Marcinkowski
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Corresponding author

Correspondence to Salah Alrabeei .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

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

    Ewa Deelman

  3. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Alrabeei, S., Jokar, M., Marcinkowski, L. (2020). Additive Average Schwarz with Adaptive Coarse Space for Morley FE. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_25

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  • DOI: https://doi.org/10.1007/978-3-030-43222-5_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43221-8

  • Online ISBN: 978-3-030-43222-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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