Authors: | Schweizer, Ben |
Title: | Effective Helmholtz problem in a domain with a Neumann sieve perforation |
Language (ISO): | en |
Abstract: | A first order model for the transmission of waves through a sound-hard perforation along an interface is derived. Mathematically, we study the Neumann problem for the Helmholtz equation in a complex geometry, the domain contains a periodic array of inclusions of size ε > 0 along a co-dimension 1 manifold. We derive effective equations that describe the limit as ε → 0. At leading order, the Neumann sieve perforation has no effect; the corrector is given by a Helmholtz equation on the unperturbed domain with jump conditions across the interface. The corrector equations are derived with unfolding methods in L^1-based spaces. |
Subject Headings: | Helmholtz equation perforation thin layer transmission condition |
URI: | http://hdl.handle.net/2003/37860 http://dx.doi.org/10.17877/DE290R-19847 |
Issue Date: | 2018-12-06 |
Appears in Collections: | Preprints der Fakultät für Mathematik Schweizer, Ben Prof. Dr. |
Files in This Item:
File | Description | Size | Format | |
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Preprint 2018-08.pdf | DNB | 452.13 kB | Adobe PDF | View/Open |
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