Approximate models for wave propagation across thin periodic interfaces

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• 作者：Bé ; rangè ; re Delourme^a ; ^b ; ^{berangere.delourme@gmail.com} ; Houssem Haddar^b ; Patrick Joly^a
• 关键词：Effective transmission conditions ; Periodic thin interfaces ; Matched asymptotic expansions ; Homogenization ; Helmholtz equation
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：2012
• 期刊代码：29_00217824
• 类别：mt
• 出版时间：July, 2012
• 卷：98
• 期：1
• 页码：28-71
• 文件大小：579 K

摘要

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.