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Solving the Signorini problem on the basis of domain decomposition techniques. (English) Zbl 0915.73077
Summary: 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, a 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 Signorini problem as well as for contact problems in plane elasticity confirm the theoretical analysis.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
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