Using perfectly matched layers for the computation of resonances in open systems typically produces artificial or spurious resonances. We analyze the dependency of these artificial resonances with respect to the discretization parameters and the complex scaling function. In particular, we study the differences between a standard frequency independent complex scaling and a frequency dependent one. While the standard scaling leads to a linear eigenvalue problem, the frequency dependent scaling leads to a polynomial one. Our studies show that the location of artificial resonances is more convenient for the frequency dependent scaling than for a standard scaling. Moreover, the artificial resonances of a frequency dependent scaling are less sensitive to the discretization parameters. Hence, the use of a frequency dependent scaling simplifies the choice of the corresponding discretization parameters.

中文翻译：

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使用具有频率相关缩放函数的完美匹配层计算散射共振

在开放系统中使用完美匹配层计算共振通常会产生人工或虚假共振。我们分析了这些人工共振对离散化参数和复杂缩放函数的依赖性。特别是，我们研究了标准频率独立复标度和频率相关复标度之间的差异。虽然标准缩放会导致线性特征值问题，但频率相关缩放会导致多项式问题。我们的研究表明，人工共振的位置对于频率相关的缩放比标准缩放更方便。此外，频率相关缩放的人工共振对离散化参数不太敏感。因此，