In many engineering applications, the solution of acoustic wave problems in the infinite domain is required over a broad frequency range with densely sampled increments. In order to achieve efficient numerical simulations via a spatial discretization, e.g. finite element method, additional artificial absorbing boundaries are necessary to truncate the computational domain into appropriate bounded sizes. One of the most commonly used non-reflecting techniques to attenuate propagating waves is known as the perfectly matched layer. However, the system matrices arising from the finite element treatment of the Helmholtz equation in the absorbing layers are frequency-dependent, implying that they must be formed and inverted at each frequency of interest. Such a procedure is rather troublesome for frequency sweeps. To address this, a surrogate of perfectly matched layers is proposed, which enables the corresponding system matrices to be independent of the frequency. Moreover, it avoids the use of a relatively large computational domain and relatively thick enclosed layers at low frequencies, thus improving the ability of perfectly matched layers across the entire frequency range. After that, an adaptive projection-based model order reduction scheme is further developed to reduce the computational complexity of exterior acoustic systems. A robust error indicator based on the relative error of two constructed reduced order models is accordingly introduced. The performance of the present solution framework is discussed and compared with other implementation strategies, in the context of multi-frequency solution of two-dimensional test models with single or multiple scatterers.

中文翻译：

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与频率无关的吸收函数替代物，用于外部声学中的完美匹配层


在许多工程应用中，需要在很宽的频率范围内以密集采样的增量求解无限域中的声波问题。为了通过空间离散化（例如有限元方法）实现高效的数值模拟，需要额外的人工吸收边界来将计算域截断为适当的有界大小。衰减传播波的最常用非反射技术之一称为完美匹配层。然而，吸收层中亥姆霍兹方程的有限元处理产生的系统矩阵是频率依赖性的，这意味着它们必须在每个感兴趣的频率上形成和反转。这样的过程对于频率扫描来说相当麻烦。为了解决这个问题，提出了一个完美匹配层的代理，这使得相应的系统矩阵独立于频率。此外，它避免了在低频下使用相对较大的计算域和相对较厚的封闭层，从而提高了在整个频率范围内完美匹配层的能力。之后，进一步开发了一种基于自适应投影的模型降阶方案，以降低外部声学系统的计算复杂度。因此，引入了一个基于两个构建的降阶模型的相对误差的稳健误差指标。在具有单个或多个散射体的二维测试模型的多频求解的背景下，讨论了当前解决方案框架的性能，并与其他实现策略进行了比较。