On the homogenization of thin perforated walls of finite length
Please always quote using this URN:urn:nbn:de:0296-matheon-13674
- The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes into account the boundary layer effect occurring in the vicinity of the periodic layer as well as the corner singularities appearing in the neighborhood of the extremities of the layer. Our approach combines mixes the method of matched asymptotic expansions and the method of periodic surface homogenization.
Author: | Bérangère Delourme, Kersten Schmidt, Adrien Semin |
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URN: | urn:nbn:de:0296-matheon-13674 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2015/12/28 |
Release Date: | 2015/12/28 |
Tag: | Asymptotic analysis; Periodic surface homogenization; Singular asymptotic expansions |
Institute: | Technische Universität Berlin |
Project: | B Networks / B-MI2 Optimized noise reduction in transportation and interior spaces |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A20 Analytic methods, singularities |
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C20 Asymptotic expansions | |
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] | |
Preprint Number: | 1095 |