Optimization with PDE Constraints

0433801 - ÚTIA 2015 RIV DE eng M - Monography Chapter
Outrata, Jiří - Beremlijski, P. - Haslinger, J. - Pathó, R.
Numerical solution of 2D Contact Shape Optimization Problems Involving a Solution-Dependent Coefficient of Friction.
Optimization with PDE Constraints. Heidelberg: Springer, 2014 - (Hoppe, R.), s. 1-24. Lecture Notes in Computational Science and Engineering, 101. ISBN 978-3-319-08024-6
R&D Projects: GA ČR(CZ) GAP201/12/0671
Institutional support: RVO:67985556
Keywords : Frictional contact * Nonsmooth analysis * Shape optimization
OECD category: Pure mathematics
http://library.utia.cas.cz/separaty/2014/MTR/outrata-0433801.pdf

This contribution deals with numerical solution of shape optimization problems in frictional contact mechanics. The state problem in our case is given by 2D static Signorini problems with Tresca friction and a solution-dependent coefficient of friction. A suitable Lipschitz continuity assumption on the coefficient of friction is made, ensuring unique solvability of the discretized state problems and Lipschitz continuity of the corresponding control-to-state mapping. The discrete shape optimization problem can be transformed into a nonsmooth minimization problem and handled by the bundle trust method. In each step of the method, the state problem is solved by the method of successive approximations and necessary subgradient information is computed using the generalized differential calculus of B. Mordukhovich.
Permanent Link: http://hdl.handle.net/11104/0239357