High order asymptotics for wave propagation across thin periodic interfaces

Article type: Research Article

Authors: Claeys, Xavier | Delourme, Bérangère^{; ; ;}

Affiliations: Université de Toulouse, ISAE, Toulouse, France | INRIA Rocquencourt, Domaine de Voluceau, Le Chesnay, France | INRIA Saclay Ile de France and Ecole Polytechnique, CMAP, Palaiseau, France | CEA, LETI, MINATEC, Grenoble, France

Note: [] Corresponding author: Bérangère Delourme, ACM Caltech, 1200 E California Blvd., Pasadena, CA 91106, USA. Tel.: +1 626 395 3531; E-mail: delourme@caltech.edu

Abstract: This work deals with the scattering of acoustic waves by a thin ring that contains many regularly-spaced heterogeneities. We provide and justify a complete description of the solution with respect to the period and the thickness of the heterogeneities. Our approach mixes matched asymptotic expansions and homogenization theory.

Keywords: periodic thin interfaces, matched asymptotic expansions, homogenization, Helmholtz equation

DOI: 10.3233/ASY-2012-1150

Journal: Asymptotic Analysis, vol. 83, no. 1-2, pp. 35-82, 2013