A method to build non-scattering perturbations of two-dimensional acoustic waveguides
january, 2015
Type de publication :
Article (revues avec comité de lecture)
Journal :
Math. meth. appl. sci., vol. 40, pp. 335–349
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Mots clés :
waveguide,modal analysis,scattering matrix,asymptotic analysis,cloaking, fixed-point algorithm
Résumé :
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={Math. meth. appl. sci. }, year={2015 }, month={1}, volume={40 }, pages={335–349}, }