论文标题
在3D双周期表面散射问题中完美匹配的层的高阶收敛性
Higher order convergence of perfectly matched layers in 3D bi-periodic surface scattering problems
论文作者
论文摘要
完美匹配的层（PML）是在无界域中波散射的截断中非常流行的工具。在Chandler-Wilde＆Monk等。 2009年，作者提出了一个猜想，该猜想是针对粗糙表面的散射问题，PML相对于任何紧凑型子集中的PML参数呈指数收敛。在作者的上一篇论文（Zhang等，2022）中，当波数不是半整数时，已证明了在二维空间中的周期性表面证明了这一结果。在本文中，我们证明该方法在3D双期表面散射问题中具有高阶收敛速率。我们扩展了2D结果，并证明当波数小于$ 0.5 $时，指数融合仍然存在。对于Lareger波数，尽管不再证明指数收敛，但我们能够证明PML方法的高阶收敛性。
The perfectly matched layer (PML) is a very popular tool in the truncation of wave scattering in unbounded domains. In Chandler-Wilde & Monk et al. 2009, the author proposed a conjecture that for scattering problems with rough surfaces, the PML converges exponentially with respect to the PML parameter in any compact subset. In the author's previous paper (Zhang et al. 2022), this result has been proved for periodic surfaces in two dimensional spaces, when the wave number is not a half integer. In this paper, we prove that the method has a high order convergence rate in the 3D bi-periodic surface scattering problems. We extend the 2D results and prove that the exponential convergence still holds when the wavenumber is smaller than $0.5$. For lareger wavenumbers, although exponential convergence is no longer proved, we are able to prove that a higher order convergence for the PML method.
