Translator Disclaimer
April, 2020 Topological Sensitivity Analysis and Kohn-Vogelius Formulation for Detecting a Rigid Inclusion in an Elastic Body
Mourad Hrizi
Taiwanese J. Math. 24(2): 439-482 (April, 2020). DOI: 10.11650/tjm/190705

Abstract

Our main interest in this work is to detect a rigid inclusion immersed in an isotropic elastic body $\Omega$ from a single pair of Cauchy data on $\partial \Omega$ in two dimensions. We want to completely characterize the unknown rigid inclusion, namely, the shape and the location of inclusion. The idea is to rewrite the inverse problem as an optimization problem, where an energy like functional is minimized with respect to the presence of a small inclusion. A topological sensitivity analysis is derived for an energy like functional. We proposed a non-iterative reconstruction algorithm based on the topological gradient concept. The unknown rigid inclusion is defined by a level curve of a scalar function. The proposed numerical approach is very robust with respect to noisy data. Finally, in order to show the efficiency and accuracy of the proposed algorithm, we present some numerical results.

Citation

Download Citation

Mourad Hrizi. "Topological Sensitivity Analysis and Kohn-Vogelius Formulation for Detecting a Rigid Inclusion in an Elastic Body." Taiwanese J. Math. 24 (2) 439 - 482, April, 2020. https://doi.org/10.11650/tjm/190705

Information

Received: 22 March 2019; Revised: 6 July 2019; Accepted: 15 July 2019; Published: April, 2020
First available in Project Euclid: 9 August 2019

zbMATH: 07192943
MathSciNet: MR4078206
Digital Object Identifier: 10.11650/tjm/190705

Subjects:
Primary: 35R30, 49Q10, 49Q12, 74P15

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
44 PAGES


SHARE
Vol.24 • No. 2 • April, 2020
Back to Top