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Solving the signorini problem on the basis of domain decomposition techniques

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Abstract

The finite element discretization of the Signorini Problem leads to a large scale constrained minimization problem. To improve the convergence rate of the projection method preconditioning must be developed. To be effective, the relative condition number of the system matrix with respect to the preconditioning matrix has to be small and the applications of the preconditioner as well as the projection onto the set of feasible elements have to be fast computable. In this paper, we show how to construct and analyze such preconditioners on the basis of domain decomposition techniques. The numerical results obtained for the Signorini problem as well as for contact problems in plane elasticity confirm the theoretical analysis quite well.

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Authors and Affiliations

  1. Institut für Mathematik, Johannes Kepler Universität Linz, Altenbergerstraße 69, 4040, Linz, Austria

    J. Schöberl

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  1. J. Schöberl
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This research has been supported by the Austrian Science Foundation — ‘Fonds zur Förderung der wissenschaftlichen Forschung (FWF)’ — under project grant P10643-TEC.

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Schöberl, J. Solving the signorini problem on the basis of domain decomposition techniques. Computing 60, 323–344 (1998). https://doi.org/10.1007/BF02684379

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  • DOI: https://doi.org/10.1007/BF02684379

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