论文标题
在周期性层中Helmholtz方程的均质化研究法拉第笼状的屏蔽效应
Homogenization of Helmholtz equation in a periodic layer to study Faraday cage-like shielding effects
论文作者
论文摘要
这项工作是由法拉第笼效应的动机。我们考虑3D域上的Helmholtz方程，该域中包含厚度$δ\ ll 1 $的薄界面。该层在平面方向上具有$δ-$周期性结构，并且在第三方向上是圆柱形的。周期层具有一个连接的组件和一组孤立区域。薄层中的孤立区域代表空气或液体，连接的组件表示$δ$厚度的实心金属网格。主要问题是由空气和网格中系数的对比度所产生的，并且零订单项在连接的遮挡中具有复杂的值系数，而补充中的实现值。提供了有关$δ\至0 $的渐近分析，并在界面上的dirichlet条件获得了极限Helmholtz问题。定期展开方法用于找到限制。
The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3D-domain containing a thin heterogeneous interface of thickness $δ\ll 1$. The layer has a $δ-$periodic structure in the in-plane directions and is cylindrical in the third direction. The periodic layer has one connected component and a collection of isolated regions. The isolated region in the thin layer represents air or liquid, and the connected component represents a solid metal grid with a $δ$ thickness. The main issue is created by the contrast of the coefficients in the air and in the grid and that the zero-order term has a complex-valued coefficient in the connected faze while a real-valued in the complement. An asymptotic analysis with respect to $δ\to 0$ is provided, and the limit Helmholtz problem is obtained with the Dirichlet condition on the interface. The periodic unfolding method is used to find the limit.
