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Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain

Title data

Schiela, Anton ; Stöcklein, Matthias:
Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.
University Bayreuth , 2019 . - 21 p.

Official URL: Volltext

Project information

Project financing: Deutsche Forschungsgemeinschaft
DFG grant SCHI 1379/2-1 within the priority programme SPP 1962

Abstract in another language

Optimal control of hyperelastic contact problems in the regime of finite strains combines various severe theoretical and algorithmic difficulties. Apart from being large scale, the main source of difficulties is the high nonlinearity and non-convexity of the elastic energy functional which precludes uniqueness of solutions and simple local sensitivity results. In addition, the contact conditions add non-smoothness
to the overall problem.

In this paper, we discuss algorithmic approaches to address these issues. In particular, the non-smoothness is tackled by a path-following approach, whose theoretical properties are reviewed. The subproblems are highly nonlinear optimal control problems, which can be solved by an affine invariant composite step method. For increased robustness and efficiency this method has to be adapted to the particular problem, taking into account its large scale nature, its function space structure and its non-convexity.

Further data

Item Type: Preprint, postprint
Keywords: nonlinear elasticity; optimal control; contact problem
Subject classification: 49M37, 90C55
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics) > Chair Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 14 Sep 2019 21:00
Last Modified: 16 Sep 2019 06:35
URI: https://eref.uni-bayreuth.de/id/eprint/52240