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BDDC for Nonsymmetric Positive Definite and Symmetric Indefinite Problems

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Domain Decomposition Methods in Science and Engineering XVIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 70))

Summary

The balancing domain decomposition methods by constraints are extended to solving both nonsymmetric, positive definite and symmetric, indefinite linear systems. In both cases, certain nonstandard primal constraints are included in the coarse problems of BDDC algorithms to accelerate the convergence. Under the assumption that the subdomain size is small enough, a convergence rate estimate for the GMRES iteration is established showing that the rate is independent of the number of subdomains and depends only slightly on the subdomain problem size. Numerical experiments for several two-dimensional examples illustrate the fast convergence of the proposed algorithms.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California and Lawrence Berkeley National Laboratory, 94720-3840, CA, Berkeley, USA

    Tu Xuemin

  2. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Jing Li

Authors
  1. Tu Xuemin
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  2. Jing Li
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Corresponding author

Correspondence to Tu Xuemin .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Ross Building - Givat Ram Campus, 91904, Jerusalem, Israel

    Michel Bercovier

  2. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Genève 24, Switzerland

    Martin J. Gander

  3. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin-Dahlem, Germany

    Ralf Kornhuber

  4. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Olof Widlund

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Xuemin, T., Li, J. (2009). BDDC for Nonsymmetric Positive Definite and Symmetric Indefinite Problems. In: Bercovier, M., Gander, M.J., Kornhuber, R., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02677-5_7

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