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Domain Decomposition Methods in Science and Engineering XX pp 39–49Cite as

Scalable Domain Decomposition Algorithms for Contact Problems: Theory, Numerical Experiments, and Real World Problems

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

Summary

We review our results related to the development of theoretically supported scalable algorithms for the solution of large scale contact problems of elasticity. The algorithms combine the Total FETI/BETI based domain decomposition method adapted to the solution of 2D and 3D multibody contact problems of elasticity, both frictionless and with friction, with our in a sense optimal algorithms for the solution of resulting quadratic programming and QPQC problems. Rather surprisingly, the theoretical results are qualitatively the same as the classical results on scalability of FETI/BETI for linear elliptic problems. The efficiency of the method is demonstrated by results of parallel numerical experiments for contact problems of linear elasticity discretized by more than 11 million variables in 3D and 40 million variables in 2D.

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Acknowledgements

This research has been supported by the grants GA CR No. 201/07/0294 and ME CR No. MSM6198910027.

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Authors and Affiliations

  1. Dept. of Appl. Math., VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Z. Dostál, T. Kozubek, T. Brzobohatý, A. Markopoulos, M. Sadowská & V. Vondrák

Authors
  1. Z. Dostál
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  2. T. Kozubek
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  3. T. Brzobohatý
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  4. A. Markopoulos
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  5. M. Sadowská
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  6. V. Vondrák
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Corresponding author

Correspondence to Z. Dostál .

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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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Dostál, Z., Kozubek, T., Brzobohatý, T., Markopoulos, A., Sadowská, M., Vondrák, V. (2013). Scalable Domain Decomposition Algorithms for Contact Problems: Theory, Numerical Experiments, and Real World 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_4

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