Issue |
RAIRO-Oper. Res.
Volume 56, Number 5, September-October 2022
|
|
---|---|---|
Page(s) | 3689 - 3709 | |
DOI | https://doi.org/10.1051/ro/2022168 | |
Published online | 31 October 2022 |
Coupled complex boundary method for a geometric inverse source problem
Faculty of Sciences and Techniques, Sultan Moulay Slimane University, Beni Mellal, Morocco
* Corresponding author: lekbir.afraites@gmail.com
Received:
27
December
2021
Accepted:
24
September
2022
This work deals with a geometric inverse source problem. It consists in recovering the characteristic function of an unknown inclusion based on boundary measurements. We propose a new reconstruction method based on the CCBM and the shape gradient method, the inverse problem is formulated as a shape optimization one, corresponding to a coupled complex boundary state problem. Well posedness and existence results are presented. A computed expression for the shape gradient is used to implement a gradient algorithm. The efficiency and accuracy of the reconstruction algorithm are illustrated by some numerical results, and a comparison between CCBM, Least-squares and Kohn-Vogeluis methods is presented.
Mathematics Subject Classification: 65K05 / 65K10 / 49J20 / 49J50
Key words: Coupled complex boundary method / inverse geometric source problem / shape optimization / shape derivative / adjoint method
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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