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

Anne-Sophie Bonnet-BenDhia, Eric Lunéville, Yves Mbeutcha and 
Sergei Nazarov
january, 2015
Publication type:
Paper in peer-reviewed journals
Journal:
Mathematical Methods in the Applied Sciences
Keywords :
waveguide,modal analysis,scattering matrix,asymptotic analysis,cloaking, fixed-point algorithm
Abstract:
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 (1]. 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.
BibTeX:
@article{Bon-Lun-Mbe-Naz-2015,
    author={Anne-Sophie Bonnet-BenDhia and Eric Lunéville and Yves 
           Mbeutcha and Sergei Nazarov },
    title={A method to build non-scattering perturbations of 
           two-dimensional acoustic waveguides },
    doi={10.1002/mma.3447 },
    journal={Mathematical Methods in the Applied Sciences },
    year={2015 },
    month={1},
}