Approximate Models for Wave Propagation Across Thin Periodic Interfaces

Bérangère Delourme 1, 2, * Houssem Haddar 3 Patrick Joly 2
* Corresponding author
2 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
3 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : This work deals with the scattering of acoustic waves by a thin ring which contains many regularly-spaced heterogeneties. We provide a complete description of the asymptotic of the solution with respect to the period and the thickness of the heterogeneities. Then, we build a simplified model replacing the thin perforated ring by an effective transmission condition. We pay particular attention to the stabilization of the effective transmission condition. Error estimates and numerical simulations are carried out to validate the accuracy of the model.
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Bérangère Delourme, Houssem Haddar, Patrick Joly. Approximate Models for Wave Propagation Across Thin Periodic Interfaces. [Research Report] RR-7197, INRIA. 2010. ⟨inria-00456200⟩

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