TY - GEN A1 - Delourme, Bérangère A1 - Schmidt, Kersten A1 - Semin, Adrien T1 - On the homogenization of thin perforated walls of finite length T2 - Asymptotic Analysis N2 - 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 the method of matched asymptotic expansions and the method of periodic surface homogenization. KW - asymptotic analysis KW - periodic surface homogenization KW - singular asymptotic expansions Y1 - 2016 UR - http://content.iospress.com/articles/asymptotic-analysis/asy1350 U6 - https://doi.org/10.3233/ASY-151350 SN - 0921-7134 SN - 1875-8576 VL - 97 IS - 3-4 SP - 211 EP - 264 ER - TY - RPRT A1 - Schmidt, Kersten A1 - Semin, Adrien A1 - Delourme, Bérangère T1 - On the homogenization of the Helmholtz problem with thin perforated walls of finite length N2 - On the homogenization of the Helmholtz problem with thin perforated walls of finite length Y1 - 2016 UR - https://arxiv.org/abs/1611.06001 ER - TY - RPRT A1 - Schmidt, Kersten A1 - Semin, Adrien A1 - Delourme, Bérangère T1 - When a thin periodic layer meets corners: asymptotic analysis of a singular Poisson problem N2 - 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 the method of matched asymptotic expansions and the method of periodic surface homogenization, and a complete justification is included in the paper or its appendix. KW - asymptotic analysis KW - periodic surface homogenization KW - singular asymptotic expansions Y1 - 2015 UR - https://arxiv.org/abs/1506.06964 ER -