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Fast and accurate algorithm for cavities reconstruction in an elasticity problem
Author(s) -
Hrizi Mourad,
Hassine Maatoug,
Abdelwahed Mohamed,
Chorfi Nejmeddine
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5706
Subject(s) - mathematics , linear elasticity , inverse problem , elasticity (physics) , isotropy , topology optimization , topology (electrical circuits) , algorithm , mathematical optimization , displacement field , boundary value problem , geometry , mathematical analysis , finite element method , combinatorics , physics , materials science , quantum mechanics , composite material , thermodynamics
The aim of this work is to reconstruct the location and geometry of a cavity C embedded in a linear isotropic material Ω via an exterior boundary measurement of the displacement field. The considered problem is governed by the linear elasticity system. This inverse problem of geometry reconstruction (ie, location and shape) is formulated as a topology optimization one and solved by minimizing a Kohn‐Vogelius type functional with the help of the topological sensitivity method. Some numerical results are presented using a noniterative geometric algorithm.