Transmission eigenvalues with artificial background for explicit material index identification

Lorenzo Audibert; Lucas Chesnel; Houssem Haddar

doi:10.1016/j.crma.2018.04.015

Partial differential equations/Numerical analysis

Transmission eigenvalues with artificial background for explicit material index identification

Presented by: the Editorial Board

Lorenzo Audibert ^1,²; Lucas Chesnel ²; Houssem Haddar ²

¹ Department STEP, EDF R&D, 6, quai Watier, 78401 Chatou cedex, France
² INRIA/Centre de mathématiques appliquées, École polytechnique, Université Paris-Saclay, route de Saclay, 91128 Palaiseau, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 626-631.

Abstract
Résumé

We are interested in the problem of retrieving information on the refractive index n of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on n and that can be determined from the knowledge of the farfield operator F. In this note, we explain how to modify F into a farfield operator $F^{art} = F - \tilde{F}$ , where $\tilde{F}$ is computed numerically, corresponding to well-chosen artificial background and for which the associated TEs provide more accessible information on n.

Nous souhaitons retrouver l'indice n d'une inclusion pénétrable dans un milieu de référence connu à partir de la donnée de champs lointains associés à des ondes planes incidentes. Pour ce faire, nous utilisons les valeurs propres de transmission (VPT) qui dépendent de n et qui peuvent être déterminées à partir de l'opérateur de champ lointain F. Dans cette note, nous expliquons comment modifier F en un opérateur de champ lointain $F^{art} = F - \tilde{F}$ , où $\tilde{F}$ est calculé numériquement, correspondant à un milieu de référence artificiel et pour lequel les VPT associées fournissent une information plus directe sur n.

Received: 2017-11-08
Accepted: 2018-04-12
Published online: 2018-04-25

DOI: 10.1016/j.crma.2018.04.015

Author's affiliations:

Lorenzo Audibert ^{1, 2}; Lucas Chesnel ²; Houssem Haddar ²

¹ Department STEP, EDF R&D, 6, quai Watier, 78401 Chatou cedex, France
² INRIA/Centre de mathématiques appliquées, École polytechnique, Université Paris-Saclay, route de Saclay, 91128 Palaiseau, France

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     author = {Lorenzo Audibert and Lucas Chesnel and Houssem Haddar},
     title = {Transmission eigenvalues with artificial background for explicit material index identification},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {626--631},
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     number = {6},
     year = {2018},
     doi = {10.1016/j.crma.2018.04.015},
     language = {en},
}

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Lorenzo Audibert; Lucas Chesnel; Houssem Haddar. Transmission eigenvalues with artificial background for explicit material index identification. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 626-631. doi : 10.1016/j.crma.2018.04.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.015/

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