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TFETI Scalable Solvers for Transient Contact 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))

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Summary

We review our results obtained by application of the TFETI domain decomposition method to implement the time step of the Newmark scheme for the solution of transient contact problems without friction. If the ratio of the decomposition and discretization parameters is kept uniformly bounded as well as the ratio of the time and space discretization, then the cost of the time step is proved to be proportional to the number of nodal variables. The algorithm uses our MPRGP algorithm for the solution of strictly convex bound constrained quadratic programming problems with optional preconditioning by the conjugate projector to the subspace defined by the trace of the rigid body motions on the artificial subdomain interfaces. The optimality relies on our results on quadratic programming, the theory of the preconditioning by a conjugate projector for nonlinear problems, and the classical bounds on the spectrum of the mass and stiffness matrices. The results are confirmed by numerical solution of 3D transient contact problems.

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Bibliography

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Acknowledgements

The work is supported by the project of Ministry of Education of the Czech Republic MSM6198910027 and by the project 101/08/0574 of the Grant Agency of the Czech Republic.

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Authors and Affiliations

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

    T. Kozubek, Z. Dostál, T. Brzobohatý, A. Markopoulos & O. Vlach

Authors
  1. T. Kozubek
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  2. Z. Dostál
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  3. T. BrzobohatĂ˝
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  4. A. Markopoulos
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  5. O. Vlach
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Corresponding author

Correspondence to T. Kozubek .

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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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Kozubek, T., Dostál, Z., Brzobohatý, T., Markopoulos, A., Vlach, O. (2013). TFETI Scalable Solvers for Transient Contact 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_38

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