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A method to build non‐scattering perturbations of two‐dimensional acoustic waveguides
Author(s) -
BonnetBen Dhia A. S.,
Lunéville E.,
Mbeutcha Y.,
Nazarov S. A.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3447
Subject(s) - reflection (computer programming) , point (geometry) , waveguide , argument (complex analysis) , scattering , set (abstract data type) , field (mathematics) , acoustics , computer science , presentation (obstetrics) , mathematical analysis , mathematics , calculus (dental) , physics , optics , geometry , pure mathematics , medicine , biochemistry , chemistry , dentistry , programming language , radiology
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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