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Engineering Multibody Contact Problems Solved by Scalable TBETI

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Fast Boundary Element Methods in Engineering and Industrial Applications

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 63))

Abstract

We review our recent results in the development of scalable total BETI (TBETI) based domain decomposition algorithms for the solution of multibody contact problems of linear elastostatics. We report the scalability of our algorithms for the frictionless problems and the problems with a given (Tresca) friction. Our main tool is the preconditioning by a natural coarse grid of the rigid body motions combined with the BETI methodology and with our in a sense optimal algorithms for the minimization of strictly convex quadratic function subject to separable inequality and linear equality constraints. The analysis admits floating bodies. The theoretical results are verified by numerical experiments, where we also use our algorithms to implement effectively the fixed point iterations for the solution of problems with the Coulomb friction. The power of the method is demonstrated on a real world problem.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, FEECS, VŠB–TU Ostrava, 17. listopadu 15, 70833, Ostrava, Czech Republic

    Marie Sadowská, Zdeněk Dostál, Tomáš Kozubek & Jiří Bouchala

  2. Department of Mechanics, FME, VŠB–TU Ostrava, 17. listopadu 15, 70833, Ostrava, Czech Republic

    Alexandros Markopoulos

Authors
  1. Marie Sadowská
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  2. Zdeněk Dostál
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  3. Tomáš Kozubek
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  4. Alexandros Markopoulos
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  5. Jiří Bouchala
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Correspondence to Marie Sadowská .

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Editors and Affiliations

  1. Inst. Numerische Mathematik, Universität Linz, Altenbergerstr. 69, Linz, 4040, Austria

    Ulrich Langer

  2. Inst. Allgemeine Mechanik, TU Graz, Technikerstr. 4, Graz, 8010, Austria

    Martin Schanz

  3. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, 8010, Austria

    Olaf Steinbach

  4. Institut für Angewandte Analysis, und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany

    Wolfgang L. Wendland

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Sadowská, M., Dostál, Z., Kozubek, T., Markopoulos, A., Bouchala, J. (2012). Engineering Multibody Contact Problems Solved by Scalable TBETI. In: Langer, U., Schanz, M., Steinbach, O., Wendland, W. (eds) Fast Boundary Element Methods in Engineering and Industrial Applications. Lecture Notes in Applied and Computational Mechanics, vol 63. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25670-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-25670-7_8

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