A method to build non-scattering perturbations of two-dimensional acoustic waveguides

Anne-Sophie Bonnet-Ben Dhia 1 Éric Lunéville 1 Yves Mbeutcha 1 Sergei Nazarov 2, 3
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We are interested in finding deformations of the rigid wall of a two-dimensional acoustic waveguide, which are not detectable in the far field, as they produce neither reflection nor conversion of propagative modes. A proof of existence of such invisible deformations has been presented in a previous paper. It combines elements of the asymptotic analysis for small deformations and a fixed-point argument. In the present paper, we give a systematic presentation of the method, and we prove that it works for all frequencies except a discrete set. A particular attention is devoted to the practical implementation of the method. The main difficulty concerns the building of a dual family to given oscillating functions. Advantages and limits of the method are illustrated by several numerical results. Copyright © 2015 John Wiley & Sons, Ltd.
Type de document :
Article dans une revue
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, <10.1002/mma.3447>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01225313
Contributeur : Anne-Sophie Bonnet-Ben Dhia <>
Soumis le : vendredi 6 novembre 2015 - 09:33:04
Dernière modification le : samedi 18 février 2017 - 01:12:40

Identifiants

Citation

Anne-Sophie Bonnet-Ben Dhia, Éric Lunéville, Yves Mbeutcha, Sergei Nazarov. A method to build non-scattering perturbations of two-dimensional acoustic waveguides. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, <10.1002/mma.3447>. <hal-01225313>

Partager

Métriques

Consultations de la notice

102