Research output: Contribution to journal › Article
A method to build non-scattering perturbations of two-dimensional acoustic waveguides. / Bonnet-Ben Dhia, A.S.; Lunéville, E.; Mbeutcha, Y.; Nazarov, S.A.
In: Mathematical Methods in the Applied Sciences, 2015, p. None.Research output: Contribution to journal › Article
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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 -
ID: 4011979