Schweizer, Ben2019-01-082019-01-082018-12-06http://hdl.handle.net/2003/3786010.17877/DE290R-19847A 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.enHelmholtz equationperforationthin layertransmission condition610preprint