A continuation method for building invisible obstacles in waveguides

Author:

Bera Antoine1,Bonnet-Ben Dhia Anne-Sophie1,Chesnel Lucas2

Affiliation:

1. (Laboratoire Poems, CNRS/INRIA/ENSTA Paris, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91762 Palaiseau, France)

2. (INRIA/Centre de mathématiques appliquées, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France)

Abstract

Summary We consider the propagation of acoustic waves in a waveguide which is unbounded in one direction. We explain how to construct at a given wavenumber penetrable obstacles characterised by a physical coefficient $\rho$ which are invisible in various ways. In particular, we focus our attention on invisibility in reflection (the reflection matrix is zero), invisibility in reflection and transmission (the scattering matrix is the same as if there were no obstacle) and relative invisibility (two different obstacles have the same scattering matrix). To study these problems, we use a continuation method which requires to compute the scattering matrix $\mathbb{S}(\rho)$ as well as its differential with respect to the material index $d\mathbb{S}(\rho)$. The justification of the method also needs for the proof of abstract results of surjectivity of well-chosen functionals constructed from the terms of $d\mathbb{S}(\rho)$. We provide a complete proof of the results in monomode regime when the wavenumber is such that only one mode can propagate. And we give all the ingredients to implement the method in multimode regime. We end the article by presenting numerical results to illustrate the analysis.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Acoustic passive cloaking using thin outer resonators;Zeitschrift für angewandte Mathematik und Physik;2022-04-18

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