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

A.S. Bonnet-Ben Dhia, E. Lunéville, Y. Mbeutcha, S.A. Nazarov

Research output

4 Citations (Scopus)

Abstract

© 2015John Wiley & Sons, Ltd.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.
Original languageEnglish
Pages (from-to)None
JournalMathematical Methods in the Applied Sciences
DOIs
Publication statusPublished - 2015

Fingerprint

Waveguide
Acoustics
Waveguides
Perturbation
Asymptotic analysis
Far Field
Asymptotic Analysis
Fixed point
Numerical Results
Presentation
Family

Cite this

@article{9f045c420afc4b4bb6731332814a55fb,
title = "A method to build non-scattering perturbations of two-dimensional acoustic waveguides",
abstract = "{\circledC} 2015John Wiley & Sons, Ltd.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.",
author = "{Bonnet-Ben Dhia}, A.S. and E. Lun{\'e}ville and Y. Mbeutcha and S.A. Nazarov",
year = "2015",
doi = "10.1002/mma.3447",
language = "English",
pages = "None",
journal = "Mathematical Methods in the Applied Sciences",
issn = "0170-4214",
publisher = "Wiley-Blackwell",

}

TY - JOUR

T1 - A method to build non-scattering perturbations of two-dimensional acoustic waveguides

AU - Bonnet-Ben Dhia, A.S.

AU - Lunéville, E.

AU - Mbeutcha, Y.

AU - Nazarov, S.A.

PY - 2015

Y1 - 2015

N2 - © 2015John Wiley & Sons, Ltd.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.

AB - © 2015John Wiley & Sons, Ltd.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.

U2 - 10.1002/mma.3447

DO - 10.1002/mma.3447

M3 - Article

SP - None

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

ER -