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Description: |
In this talk, second-order methods for contact and friction problems in linear elasticity are developed and analyzed in infinite-dimensional function space. The main difficulty of these problems lies in the friction and contact conditions that are inherently nonlinear. We mainly consider the contact problem with Tresca friction that can be stated as nondifferentiable and constrained optimization problem. By means of the Fenchel duality theorem this problem can be reformulated as constrained optimization problem involving a smooth cost functional, which is not only of theoretical but also of practical interest. The (regularized) first-order optimality conditions can be written as nonsmooth equations using certain nonlinear complementarity functions. The resulting system can be shown to be generalized differentiable (i.e., semismooth) and thus allows for the application of a Newton-type method. The resulting algorithm is related to the primal-dual active set strategy, converges superlinearly in function space and turns out to be very efficient in numerical practice. To control the regularization parameter in our implementation we suggest an path-following strategy. The talk ends by a comprehensive report on numerical tests.
Parts of this talk are joint work with Karl Kunisch, University of Graz, Austria.
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