Journal de Mathématiques Pures et Appliquées ( IF 2.3 ) Pub Date : 2020-08-21 , DOI: 10.1016/j.matpur.2020.08.002 Ben Schweizer
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 along a co-dimension 1 manifold. We derive effective equations that describe the limit as . 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 -based spaces.
中文翻译:
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沿维1流形。我们推导了将极限描述为的有效方程。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基于空间。