SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Page 2004-2039, January 2021.
This work is dedicated to the proof of stability and convergence of the Bérenger's perfectly matched layers (PMLs) in the waveguides for an arbitrary nonnegative $L^{\infty}$ damping function. The proof relies on the Laplace-domain techniques and an explicit representation of the solution to the PML problem in the waveguide. A bound for the PML error that depends on the absorption parameter and the length of the PML is presented. Numerical experiments confirm the theoretical findings.

中文翻译：

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波导中波动方程时域完全匹配层的稳定性和收敛性分析

SIAM 数值分析杂志，第 59 卷，第 4 期，第 2004-2039 页，2021 年 1 月。
这项工作致力于证明波导中 Bérenger 完美匹配层 (PML) 的稳定性和收敛性，用于任意非负 $L^ {\infty}$ 阻尼函数。该证明依赖于拉普拉斯域技术和波导中 PML 问题解的明确表示。给出了取决于吸收参数和 PML 长度的 PML 误差界限。数值实验证实了理论发现。