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 - GEN A1 - Schmidt, Kersten A1 - Semin, Adrien T1 - Absorbing boundary conditions for the viscous acoustic wave equation T2 - Mathemtatical Methods in the Applied Sciences N2 - We consider different acoustic models with viscosity in a semi-infinite waveguide with rigid walls, for which we propose and analyse absorbing boundary conditions on a truncated subdomain. The considered models are (i) the viscous acoustic equations in a stagnant mean flow, which exhibit for small viscosities boundary layers on the infinite walls, (ii) the limit equations for vanishing viscosity and (iii) a first-order approximation for low viscosity. The limit model (i) is well known as the Helmholtz equation for the pressure with homogeneous Neumann boundary conditions. For each of these models, the absorbing conditions appear as Dirichlet-to-Neumann (DtN) maps. The DtN boundary conditions for the singularly perturbed model (i) and the approximative model (iii) tend to the DtN boundary conditions of the limit problem (ii) if the viscosity approaches zero, and, hence, provide a uniform accuracy in the viscosity. The convergence of truncated DtN boundary conditions and the behaviour for viscosities tending to zero are shown in numerical experiments. Y1 - 2016 U6 - https://doi.org/10.1002/mma.3755 SN - 1099-1476 VL - 39 IS - 17 SP - 5043 EP - 5065 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 -