Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian

Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219

Output data

Year: 2021, Volume: 30, Number: 4, Pages: 461-474 Pages count : 14 DOI: 10.1515/jiip-2020-0081

Tags

adjoint state; incompressibility; inverse identification problem; Lagrangian; saddle-point problem; shape derivative; state-constrained optimization; Stokes flow

Authors

Kovtunenko Victor A. ^1,2 , Ohtsuka Kohji ³

Affiliations

1	Institute of Hydrodynamics SB RAS
2	Institute for Mathematics and Scientific Computing, University of Graz,
3	Faculty of Information Design and Sociology, Hiroshima Kokusai Gakuin University

For Stokes equations under divergence-free and mixed boundary conditions, the inverse problem of shape identification from boundary measurement is investigated. Taking the least-square misfit as an objective function, the state-constrained optimization is treated by using an adjoint state within the Lagrange approach. The directional differentiability of a Lagrangian function with respect to shape variations is proved within the velocity method, and a Hadamard representation of the shape derivative by boundary integrals is derived explicitly. The application to gradient descent methods of iterative optimization is discussed.

Kovtunenko V.A. , Ohtsuka K.
Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian
Journal of Inverse and Ill-Posed Problems. 2021. V.30. N4. P.461-474. DOI: 10.1515/jiip-2020-0081 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000835425000001
Scopus:	2-s2.0-85098884497
Elibrary:	45025158
OpenAlex:	W3118130805

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