Dirichlet-to-Neumann operator for diffraction problems in stratified anisotropic acoustic waveguides

Antoine Tonnoir

doi:10.1016/j.crma.2015.12.018

Partial differential equations/Numerical analysis

Dirichlet-to-Neumann operator for diffraction problems in stratified anisotropic acoustic waveguides

Presented by: the Editorial Board

Antoine Tonnoir ^1,²

¹ POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA, Palaiseau, France
² INRIA Saclay Île-de-France, Palaiseau, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 383-387.

Abstract
Résumé

The purpose of this note is to construct a Dirichlet-to-Neumann operator for the diffraction problem in stratified anisotropic acoustic waveguides. The key idea consists in using an adapted change of coordinates that enables to recover the completeness and the orthogonality of the modes on “deformed” cross-sections of the waveguide.

Le but de cette note est de construire un opérateur Dirichlet-to-Neumann pour le problème de diffraction dans un guide d'ondes acoustique anisotrope stratifié. Le point clé consiste à utiliser un changement de coordonnées adapté qui permet de retrouver à la fois des propriétés de complétude et d'orthogonalité des modes sur une section « déformée » du guide d'ondes.

Received: 2015-09-09
Accepted: 2015-12-04
Published online: 2016-02-09

DOI: 10.1016/j.crma.2015.12.018

Author's affiliations:

Antoine Tonnoir ^{1, 2}

¹ POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA, Palaiseau, France
² INRIA Saclay Île-de-France, Palaiseau, France

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     title = {Dirichlet-to-Neumann operator for diffraction problems in stratified anisotropic acoustic waveguides},
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Antoine Tonnoir. Dirichlet-to-Neumann operator for diffraction problems in stratified anisotropic acoustic waveguides. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 383-387. doi : 10.1016/j.crma.2015.12.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.018/

References
Cited by

[1] C.P. Berraquero; A. Maurel; P. Petitjeans; V. Pagneux Experimental realization of a water-wave metamaterial shifter, Physical Review E, Volume 88 (2013) no. 5

[2] A. Bonnet-Ben Dhia; G. Legendre An alternative to the Dirichlet-to-Neumann maps for waveguides, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011) no. 17–18, pp. 1005-1009

[3] H. Chen; C.T. Chan Acoustic cloaking and transformation acoustics, J. Phys., Volume 43 (2010) no. 11

[4] D. Givoli Numerical Method for Problems in Infinite Domains, Elsevier Science, Amsterdam, 1992

[5] C. Goldstein A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains, Math. Comput., Volume 39 (1982) no. 160, pp. 309-324

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