Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Slim Chaabane; Mohamed Jaoua

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 3, page 707-722
  • ISSN: 0764-583X

Abstract

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This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not on its Lagrangian derivative u1(θ).

How to cite

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Chaabane, Slim, and Jaoua, Mohamed. "Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini." ESAIM: Mathematical Modelling and Numerical Analysis 34.3 (2010): 707-722. <http://eudml.org/doc/197431>.

@article{Chaabane2010,
abstract = { This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not on its Lagrangian derivative u1(θ). },
author = {Chaabane, Slim, Jaoua, Mohamed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Geometrical inverse problems; identification; Signorini type boundary conditions; unknown boundary; domaine derivatives; Kohn-Vogelius function; optimal shape design.; geometrical inverse problems; Signorini type boundary conditions; domain derivative; Kohn-Vogelius function; optimal shape design; numerical examples; gradient algorithm},
language = {eng},
month = {3},
number = {3},
pages = {707-722},
publisher = {EDP Sciences},
title = {Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini},
url = {http://eudml.org/doc/197431},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Chaabane, Slim
AU - Jaoua, Mohamed
TI - Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 3
SP - 707
EP - 722
AB - This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not on its Lagrangian derivative u1(θ).
LA - eng
KW - Geometrical inverse problems; identification; Signorini type boundary conditions; unknown boundary; domaine derivatives; Kohn-Vogelius function; optimal shape design.; geometrical inverse problems; Signorini type boundary conditions; domain derivative; Kohn-Vogelius function; optimal shape design; numerical examples; gradient algorithm
UR - http://eudml.org/doc/197431
ER -

References

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  2. A. Ben Abda, S. Chaabane, F. El Dabaghi et M. Jaoua, On a non linear geometrical inverse problem of Signorini type: identifiability and stability. Math. Meth. in the Appl. Sci.21 (1998) 1379-1398.  Zbl0936.35189
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  11. K. Kunisch et X. Pan, Estimation of interfaces from boundary measurements. SIAM J. Cont. Opt.32 (1994) 867-894.  Zbl0807.35162
  12. J.L.M. Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires. Dunod, Paris (1969).  Zbl0189.40603
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  14. J.R. Roche et J. Sokolowski, Numerical methods for shape identification problems. Control and Cybernetics25 (1996) 867-894.  Zbl0876.65048
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