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Article Dans Une Revue Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Année : 2015

Multimodal method and conformal mapping for the scattering by a rough surface

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Résumé

The scattering of a wave from a periodic rough surface in two dimensions is considered. The proposed method is based on the use of a conformal mapping and of the multimodal admittance method. The use of the conformal mappings induces a spatially varying refractive index and transforms the boundary condition on the rough surface into a boundary condition on a flat surface. Then, the multimodal admittance method reduces this problem to a Riccati equation for the modal admittance matrix, which is solved numerically with a Magnus–Möbius scheme. The method is shown to converge exponentially with the number of Fourier modes. The method also allows to find geometries having trapped modes, or quasi-trapped modes, at a given frequency, by looking at singularities, or quasi-singularities, of this Riccati equation. Besides, a simple perturbation expansion, based on a small roughness approximation, is developed.

Dates et versions

hal-02991336 , version 1 (05-11-2020)

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Citer

Gael Favraud, Vincent Pagneux. Multimodal method and conformal mapping for the scattering by a rough surface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015, 471 (2175), pp.20140782. ⟨10.1098/rspa.2014.0782⟩. ⟨hal-02991336⟩
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