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Balancing Neumann-Neumann Methods for Mixed Approximations of Linear Elasticity

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Recent Developments in Domain Decomposition Methods

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 23))

Abstract

Balancing Neumann-Neumann methods are introduced and analyzed for the algebraic systems of linear equations for mixed finite element approximations of linear elasticity for incompressible and almost incompressible materials as well as composite materials with different Lamé parameters in different parts of the domain. These methods solve iteratively the saddle point Schur complement, resulting from the implicit elimination of the interior degrees of freedom, using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions. The resulting algorithm is very efficient, parallel, and robust with respect to material heterogeneities.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    Paulo Goldfeld & Olof B. Widlund

  2. Dipartimento Di Matematica, Università di Milano, Via Saldini 50, 20133, Milano, Italy

    Luca F. Pavarino

Authors
  1. Paulo Goldfeld
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  2. Luca F. Pavarino
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  3. Olof B. Widlund
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Milano, Via C. Saldini 50, 20133, Milano, Italy

    Luca F. Pavarino

  2. Seminar for Applied Mathematics, ETH Zürich, Rämistraße 101, 8092, Zürich, Switzerland

    Andrea Toselli

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© 2002 Springer-Verlag Berlin Heidelberg

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Goldfeld, P., Pavarino, L.F., Widlund, O.B. (2002). Balancing Neumann-Neumann Methods for Mixed Approximations of Linear Elasticity. In: Pavarino, L.F., Toselli, A. (eds) Recent Developments in Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56118-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-56118-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43413-9

  • Online ISBN: 978-3-642-56118-4

  • eBook Packages: Springer Book Archive

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