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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, 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.
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Submitted on : Friday, November 6, 2015 - 9:33:04 AM
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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 and Methods in Applied Sciences, World Scientific Publishing, 2015, ⟨10.1002/mma.3447⟩. ⟨hal-01225313⟩



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