论文标题
快速收敛的PML方法用于周期性表面散射：特殊情况
Fast convergent PML method for scattering with periodic surfaces: the exceptional case
论文作者
论文摘要
在作者的上一篇论文（Zhang等，2022）中，证明了指数收敛的，即与2D中周期性表面的散射问题完全匹配的层（PML）近似。但是，由于奇异点的重叠，一个特殊情况，即，当波数为半整数时，必须在证明中排除。但是，这些情况的数值结果仍然具有快速的收敛率，这激发了我们更深入地研究这些情况。在本文中，我们专注于这些案例，并证明了离散形式的快速收敛性。还提出了数值示例以支持我们的理论结果。
In the author's previous paper (Zhang et al. 2022), exponential convergence was proved for the perfectly matched layers (PML) approximation of scattering problems with periodic surfaces in 2D. However, due to the overlapping of singularities, an exceptional case, i.e., when the wave number is a half integer, has to be excluded in the proof. However, numerical results for these cases still have fast convergence rate and this motivates us to go deeper into these cases. In this paper, we focus on these cases and prove that the fast convergence result for the discretized form. Numerical examples are also presented to support our theoretical results.
