Approximate Models for Wave Propagation Across Thin Periodic Interfaces

Bérangère Delourme (1, 2) , Houssem Haddar (1) , Patrick Joly (2)

1 DeFI - Shape reconstruction and identification
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

This work deals with the scattering of acoustic waves by a thin ring that contains regularly spaced inhomogeneities. We first explicit and study the asymptotic of the solution with respect to the period and thickness of the inhomogeneities using so-called matched asymptotic expansions. We then build simplified models replacing the thin ring with Approximate Transmission Conditions that are accurate up to third order with respect to the layer width. We pay particular attention to the study of these approximate models and the quantification of their accuracy.

Domaines: Equations aux dérivées partielles [math.AP]

Bérangère Delourme, Houssem Haddar, Patrick Joly. Approximate Models for Wave Propagation Across Thin Periodic Interfaces. Journal de Mathématiques Pures et Appliquées, 2012, 98 (1), pp.28-71. ⟨10.1016/j.matpur.2012.01.003⟩. ⟨hal-00741614⟩