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A Subspace Correction Method for Nearly Singular Linear Elasticity Problems

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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))

Abstract

The focus of this work is on constructing a robust (uniform in the problem parameters) iterative solution method for the system of linear algebraic equations arising from a nonconforming finite element discretization based on reduced integration.We introduce a specific space decomposition into two overlapping subspaces that serves as a basis for devising a uniformly convergent subspace correction algorithm. We consider the equations of linear elasticity in primal variables. For nearly incompressible materials, i.e., when the Poisson ratio \(\nu\;\mathrm{approaches}\;1/2 \), this problem becomes ill-posed and the resulting discrete problem is nearly singular.

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Acknowledgements

The authors gratefully acknowledge the support by the Austrian Academy of Sciences and by the Austrian Science Fund (FWF), Project No. P19170-N18 and by the National Science Foundation NSF-DMS 0810982.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Strasse 69, 4040, Linz, Austria

    E. Karer & J. K. Kraus

  2. Penn State University, State College, University Park, USA

    L. T. Zikatanov

Authors
  1. E. Karer
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  2. J. K. Kraus
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  3. L. T. Zikatanov
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Corresponding author

Correspondence to E. Karer .

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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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Karer, E., Kraus, J.K., Zikatanov, L.T. (2013). A Subspace Correction Method for Nearly Singular Linear Elasticity Problems. 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_17

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