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A continuation method for building invisible obstacles in waveguides

Antoine Bera 1 Anne-Sophie Bonnet-Ben Dhia 1 Lucas Chesnel 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
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We consider the propagation of acoustic waves at a given wavenumber in a waveguide which is unbounded in one direction. We explain how to construct penetrable obstacles characterized by a physical coefficient ρ 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 S(ρ) as well as its differential with respect to the material index dS(ρ). The justification of the method also needs for the proof of abstract results of ontoness of well-chosen functionals constructed from the terms of dS(ρ). 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.
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Contributor : Lucas Chesnel <>
Submitted on : Monday, December 21, 2020 - 4:04:37 PM
Last modification on : Thursday, May 27, 2021 - 2:14:06 PM


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  • HAL Id : hal-02573706, version 2


Antoine Bera, Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel. A continuation method for building invisible obstacles in waveguides. Quarterly Journal of Mechanics and Applied Mathematics, Oxford University Press (OUP), 2021. ⟨hal-02573706v2⟩



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