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Robust Block Preconditioners for Biot’s Model

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

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

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Abstract

In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot’s consolidation model, where stabilized finite-element discretizations are used. The proposed block preconditioners are based on the well-posedness of the discrete linear systems. Block diagonal (norm-equivalent) and block triangular preconditioners are developed, and we prove that these methods are robust with respect to both physical and discretization parameters. Numerical results are presented to support the theoretical results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, USA

    James H. Adler & Xiaozhe Hu

  2. Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

    Francisco J. Gaspar & Carmen Rodrigo

  3. Department of Mathematics, Penn State, University Park, PA, USA

    Ludmil T. Zikatanov

Authors
  1. James H. Adler
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  2. Francisco J. Gaspar
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  3. Xiaozhe Hu
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  4. Carmen Rodrigo
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  5. Ludmil T. Zikatanov
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Corresponding authors

Correspondence to James H. Adler , Francisco J. Gaspar , Xiaozhe Hu , Carmen Rodrigo or Ludmil T. Zikatanov .

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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Adler, J.H., Gaspar, F.J., Hu, X., Rodrigo, C., Zikatanov, L.T. (2018). Robust Block Preconditioners for Biot’s Model. 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_1

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