Fast and spectrally accurate numerical methods for perforated screens (with applications to Robin boundary conditions)
Fast and spectrally accurate numerical methods for perforated screens (with applications to Robin boundary conditions)
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穿孔屏幕的快速且光谱精确的数值方法（应用于 Robin 边界条件）
DOI：
10.1093/imamat/hxaa021
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发表时间：
2020
影响因子：
1.2
通讯作者：
Colbrook M
中科院分区：
文献类型：
--
作者：
Colbrook M
本文考虑使用柔性边界条件来提供共线板有限阵列的均匀化模型，模拟穿孔屏幕或光栅。多孔筛管在形式上具有Dirichlet和Neumann边界条件的混合，而均匀化模型具有Robin边界条件。穿孔筛网在散射理论中形成了一个典型的模型，其应用范围从电磁学到空气声学。在这种情况下，对大型结构中的多孔介质的兴趣激发了对均匀化边界条件的适当性的质疑，特别是当均匀化模型改变了屏幕极端边缘考虑的结行为时。为了促进有效的研究，我们考虑了解决亥姆霍兹方程的三种数值方法：一组共线刚性板的精确问题的统一变换和迭代Wiener-Hopf方法（问题的困难几何意味着这些方法，以指数收敛，是至关重要的）和一种新的Mathieu函数搭配方法，考虑沿单个板的长度应用的变量柔度。我们详细介绍了每种方法的相对性能和实际考虑因素。通过比较用均匀化边界条件得到的共线板问题的解，我们验证了在以前的理论研究中给出的恒定柔度是适当的，即使对于有限数量的板，只要我们足够深入到渐近区域，就可以得到一个很好的解估计。我们进一步研究了在屏幕的极端端点附近逐渐缩小的顺应性，并发现带函数的逐渐缩小减少了远场近似中的误差（如果我们足够远地进入渐近区域）。我们还发现，即使进入渐近状态，板数和波数也有显著的影响。这最后两点表明了对末端效应进行建模以获得高精度结果的重要性。
This paper considers the use of compliant boundary conditions to provide a homogenized model of a finite array of collinear plates, modelling a perforated screen or grating. While the perforated screen formally has a mix of Dirichlet and Neumann boundary conditions, the homogenized model has Robin boundary conditions. Perforated screens form a canonical model in scattering theory, with applications ranging from electromagnetism to aeroacoustics. Interest in perforated media incorporated within larger structures motivates interrogating the appropriateness of homogenized boundary conditions in this case, especially as the homogenized model changes the junction behaviour considered at the extreme edges of the screen. To facilitate effective investigation we consider three numerical methods solving the Helmholtz equation: the unified transform and an iterative Wiener–Hopf approach for the exact problem of a set of collinear rigid plates (the difficult geometry of the problem means that such methods, which converge exponentially, are crucial) and a novel Mathieu function collocation approach to consider a variable compliance applied along the length of a single plate. We detail the relative performance and practical considerations for each method. By comparing solutions obtained using homogenized boundary conditions to the problem of collinear plates, we verify that the constant compliance given in previous theoretical research is appropriate to gain a good estimate of the solution even for a modest number of plates, provided we are sufficiently far into the asymptotic regime. We further investigate tapering the compliance near the extreme endpoints of the screen and find that tapering withfunctions reduces the error in the approximation of the far field (if we are sufficiently far into the asymptotic regime). We also find that the number of plates and wavenumber has significant effects, even far into the asymptotic regime. These last two points indicate the importance of modelling end effects to achieve highly accurate results.
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DOI：
--
发表时间：
1954
期刊：
影响因子：
--
作者：
A. Heins;G. L. Baldwin
通讯作者：
G. L. Baldwin
影响因子：
4.7
作者：
Colbrook, Matthew J.;Ayton, Lorna J.
通讯作者：
Ayton, Lorna J.
工商管理学士
DOI：
--
发表时间：
1984
期刊：
影响因子：
--
作者：
Baide
通讯作者：
Baide
由刚性板组成的无限光栅对声波进行散射
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
B. Erbaş;I. D. Abrahams
通讯作者：
I. D. Abrahams
带状光栅对平面波的衍射
DOI：
--
发表时间：
1990
期刊：
影响因子：
--
作者：
V. Daniele;M. Gilli;E. Viterbo
通讯作者：
E. Viterbo