@misc{DelourmeSchmidtSemin, author = {Delourme, B{\´e}rang{\`e}re and Schmidt, Kersten and Semin, Adrien}, title = {On the homogenization of thin perforated walls of finite length}, series = {Asymptotic Analysis}, volume = {97}, journal = {Asymptotic Analysis}, number = {3-4}, issn = {0921-7134}, doi = {10.3233/ASY-151350}, pages = {211 -- 264}, abstract = {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.}, language = {en} } @techreport{SchmidtSeminDelourme, author = {Schmidt, Kersten and Semin, Adrien and Delourme, B{\´e}rang{\`e}re}, title = {On the homogenization of the Helmholtz problem with thin perforated walls of finite length}, pages = {12}, abstract = {On the homogenization of the Helmholtz problem with thin perforated walls of finite length}, language = {en} } @techreport{SchmidtSeminDelourme, author = {Schmidt, Kersten and Semin, Adrien and Delourme, B{\´e}rang{\`e}re}, title = {When a thin periodic layer meets corners: asymptotic analysis of a singular Poisson problem}, pages = {58}, abstract = {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.}, language = {en} }