A 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 $\epsilon >0$ along a co-dimension 1 manifold. We derive effective equations that describe the limit as $\epsilon \to 0$. 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.

中文翻译：

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具有Neumann筛孔的区域中的有效Helmholtz问题

推导了通过界面的声波穿透波的传输的一阶模型。在数学上，我们研究了复杂几何中Helmholtz方程的Neumann问题，该域包含大小包含的周期阵列$\epsilon >0$沿维1流形。我们推导了将极限描述为的有效方程$\epsilon \to 0$。处于领先地位时，Neumann筛孔不起作用。校正器是由Helmholtz方程在无扰动区域上给出的，其中跨接口存在跳跃条件。校正器方程式通过展开方法推导${\mathrm{大号}}^{\mathrm{1个}}$基于空间。