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On an Additive Schwarz Preconditioner for the Crouzeix-Raviart Mortar Finite Element

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Domain Decomposition Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 40))

Summary

We consider an additive Schwarz preconditioner for the algebraic system resulting from the discretization of second order elliptic equations with discontinuous coefficients, using the lowest order Crouzeix-Raviart element on nonmatching meshes. The overall discretization is based on the mortar technique for coupling nonmatching meshes. A convergence analysis of the preconditioner has recently been given in Rahman et al. [2003]. In this paper, we give a matrix formulation of the preconditioner, and discuss some of its numerical properties.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Augsburg, Universitätsstr. 14, D-86159, Augsburg, Germany

    Talal Rahman

  2. LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, People's Republic of China

    Xuejun Xu

  3. Department of Mathematics, University of Houston, Calhoun Street, Houston, TX, 77204-3008, USA

    Ronald H.W. Hoppe

  4. Institute for Mathematics, University of Augsburg, Universitätsstr. 14, D-86159, Augsburg, Germany

    Ronald H.W. Hoppe

Authors
  1. Talal Rahman
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  2. Xuejun Xu
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  3. Ronald H.W. Hoppe
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Editor information

Editors and Affiliations

  1. Moffett Field, CA

    Timothy J. Barth

  2. Bonn

    Michael Griebel

  3. New York

    David E. Keyes  & Tamar Schlick  & 

  4. Espoo

    Risto M. Nieminen

  5. Leuven

    Dirk Roose

  6. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    Ralf Kornhuber

  7. Department of Mathematics, University of Houston, Philip G. Hoffman Hall 651, 77204-3008, Houston, TX, USA

    Ronald Hoppe

  8. Dassault Aviation, 78 Quai Marcel Dassault Cedex 300, 92552, St. Cloud, France

    Jacques Périaux

  9. Laboratoire Jacques-Louis Lions, Université Paris VI, 175 Rue de Chevaleret, 75013, Paris, France

    Olivier Pironneau

  10. Courant Institute of Mathematical Science, New York University, Mercer Street 251, 10012, New York, USA

    Olof Widlund

  11. Department of Mathematics Eberly College of Science, Pennsylvania Sate University, McAllister Building 218, 16802, University Park, PA, USA

    Jinchao Xu

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© 2005 Springer-Verlag Berlin Heidelberg

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Rahman, T., Xu, X., Hoppe, R.H. (2005). On an Additive Schwarz Preconditioner for the Crouzeix-Raviart Mortar Finite Element. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_33

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