A robust alternating direction numerical scheme in a shape optimization setting for solving geometric inverse problems

Fuente: arXiv

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Detalles Bibliográficos
Autores principales:	Rabago, Julius Fergy Tiongson, Hadri, Aissam, Afraites, Lekbir, Hendy, Ahmed S., Zaky, Mahmoud A.
Formato:	Preprint
Publicado:	2023
Materias:	Optimization and Control
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

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author	Rabago, Julius Fergy Tiongson Hadri, Aissam Afraites, Lekbir Hendy, Ahmed S. Zaky, Mahmoud A.
author_facet	Rabago, Julius Fergy Tiongson Hadri, Aissam Afraites, Lekbir Hendy, Ahmed S. Zaky, Mahmoud A.
contents	The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and evaluation techniques. The rationale behind this method is to achieve more accurate detection of unknown inclusions with pronounced concavities, emphasizing the aspect of shape optimization. Several numerical results to illustrate the applicability and efficiency of the method are presented for various shape detection problems. These numerical experiments are conducted in both two- and three-dimensional settings, with a focus on cases involving noise-contaminated data. The main finding of the study is that the proposed method significantly outperforms conventional shape optimization methods in reconstructing unknown cavity shapes.
format	Preprint
id	arxiv_https___arxiv_org_abs_2301_10355
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	A robust alternating direction numerical scheme in a shape optimization setting for solving geometric inverse problems Rabago, Julius Fergy Tiongson Hadri, Aissam Afraites, Lekbir Hendy, Ahmed S. Zaky, Mahmoud A. Optimization and Control The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and evaluation techniques. The rationale behind this method is to achieve more accurate detection of unknown inclusions with pronounced concavities, emphasizing the aspect of shape optimization. Several numerical results to illustrate the applicability and efficiency of the method are presented for various shape detection problems. These numerical experiments are conducted in both two- and three-dimensional settings, with a focus on cases involving noise-contaminated data. The main finding of the study is that the proposed method significantly outperforms conventional shape optimization methods in reconstructing unknown cavity shapes.
title	A robust alternating direction numerical scheme in a shape optimization setting for solving geometric inverse problems
topic	Optimization and Control
url	https://arxiv.org/abs/2301.10355

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