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Inverse problem of breaking line identification by shape optimization Full article

Journal Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219
Output data Year: 2019, Volume: 28, Number: 1, Pages: 119-135 Pages count : 17 DOI: 10.1515/jiip-2019-0047
Tags fracture; free boundary problems; inverse problems; Optimization of shapes
Authors Ghilli Daria 2 , Kunisch Karl 2 , Kovtunenko Victor A. 1,2
Affiliations
1 Lavrentyev Institute of Hydrodynamics
2 Institute for Mathematics and Scientific Computing, University of Graz

Abstract: An inverse breaking line identification problem formulated as an optimal control problem with a suitable PDE constraint is studied. The constraint is a boundary value problem describing the anti-plane equilibrium of an elastic body with a stress-free breaking line under the action of a traction force at the boundary. The behavior of the displacement is observed on a subset of the boundary, and the optimal breaking line is identified by minimizing the L 2 {L^{2}}-distance between the displacement and the observation. Then the optimal control problem is solved by shape optimization techniques via a Lagrangian approach. Several numerical experiments are carried out to show its performance in diverse situations.
Cite: Ghilli D. , Kunisch K. , Kovtunenko V.A.
Inverse problem of breaking line identification by shape optimization
Journal of Inverse and Ill-Posed Problems. 2019. V.28. N1. P.119-135. DOI: 10.1515/jiip-2019-0047 WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Jun 27, 2019
Accepted: Nov 3, 2019
Published online: Dec 4, 2019
Published print: Feb 1, 2020
Identifiers:
Web of science: WOS:000510025200010
Scopus: 2-s2.0-85076308630
Elibrary: 43210835
OpenAlex: W2991680187
Citing:
DB Citing
Scopus 8
OpenAlex 7
Elibrary 7
Web of science 6
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