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Optimization with PDE Constraints
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SYSNO ASEP 0433801 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Numerical solution of 2D Contact Shape Optimization Problems Involving a Solution-Dependent Coefficient of Friction Author(s) Outrata, Jiří (UTIA-B) RID, ORCID
Beremlijski, P. (CZ)
Haslinger, J. (CZ)
Pathó, R. (CZ)Number of authors 4 Source Title Optimization with PDE Constraints. - Heidelberg : Springer, 2014 / Hoppe R. - ISBN 978-3-319-08024-6 Pages s. 1-24 Number of pages 24 s. Number of pages 402 Publication form Print - P Language eng - English Country DE - Germany Keywords Frictional contact ; Nonsmooth analysis ; Shape optimization Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GAP201/12/0671 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000360106900002 EID SCOPUS 84921647861 DOI 10.1007/978-3-319-08025-3_1 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2015
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