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Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

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Summary

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.

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Acknowledgements

First author has been supported by MINECO grant MTM2011-27739-C04-04 and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. The work of the second and third authors was supported in part by NSF/DMS Awards 0715146 and 0915220, and by DOD/DTRA Award HDTRA-09-1-0036. The work of the fourth author was supported in part by the NSF/DMS Award 0810982.

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Authors and Affiliations

  1. Centre de Recerca Matematica (CRM), Barcelona, Spain

    Blanca Ayuso De Dios

  2. Department of Mathematics, University of California at San Diego, San Diego, California, USA

    Michael Holst

  3. Department of Mathematics, Idaho State University, Pocatello, ID, 83209-8085, USA

    Yunrong Zhu

  4. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Ludmil Zikatanov

Authors
  1. Blanca Ayuso De Dios
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  2. Michael Holst
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  3. Yunrong Zhu
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  4. Ludmil Zikatanov
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Corresponding author

Correspondence to Blanca Ayuso De Dios .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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De Dios, B.A., Holst, M., Zhu, Y., Zikatanov, L. (2013). Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_20

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