no. 6
Partial differential equations/Numerical analysis
Transmission eigenvalues with artificial background for explicit material index identification
[Une identification d'indice explicite au moyen de valeurs propres de transmission pour un milieu de référence artificiel]

Présenté par : the Editorial Board

Audibert, Lorenzo1, 2 ; Chesnel, Lucas2 ; Haddar, Houssem2
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, Tome 356 (2018) no. 6, pp. 626-631.

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 Fart=F−F˜, où F˜ est calculé numériquement, correspondant à un milieu de référence artificiel et pour lequel les VPT associées fournissent une information plus directe sur n.

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 Fart=F−F˜, where F˜ is computed numerically, corresponding to well-chosen artificial background and for which the associated TEs provide more accessible information on n.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.04.015
Audibert, Lorenzo 1, 2 ; Chesnel, Lucas 2 ; Haddar, Houssem 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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     title = {Transmission eigenvalues with artificial background for explicit material index identification},
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Audibert, Lorenzo; Chesnel, Lucas; Haddar, Houssem. Transmission eigenvalues with artificial background for explicit material index identification. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 626-631. doi : 10.1016/j.crma.2018.04.015. http://archive.numdam.org/articles/10.1016/j.crma.2018.04.015/

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