A frequency-independent absorption function surrogate for perfectly matched layer in exterior acoustics

IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Structures Pub Date : 2024-10-25 DOI:10.1016/j.compstruc.2024.107569
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Abstract

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.
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与频率无关的吸收函数替代物,用于室外声学中的完全匹配层
在许多工程应用中,需要在宽广的频率范围内以密集的采样增量解决无限域中的声波问题。为了通过空间离散化(如有限元法)实现高效的数值模拟,有必要增加人工吸收边界,将计算域截断为适当的有界尺寸。最常用的衰减传播波的非反射技术之一是完全匹配层。然而,吸收层中亥姆霍兹方程的有限元处理所产生的系统矩阵与频率有关,这意味着必须在每个感兴趣的频率上形成和反转这些矩阵。这样的程序对于频率扫描来说相当麻烦。为了解决这个问题,我们提出了一种完全匹配层的替代方法,它能使相应的系统矩阵与频率无关。此外,它还避免了在低频时使用相对较大的计算域和相对较厚的封闭层,从而提高了完全匹配层在整个频率范围内的能力。之后,进一步开发了一种基于投影的自适应模型阶次缩减方案,以降低外部声学系统的计算复杂度。相应地,还引入了一种基于两个已构建缩减阶次模型相对误差的稳健误差指标。在对具有单散射体或多散射体的二维测试模型进行多频率求解时,讨论了本求解框架的性能,并与其他实施策略进行了比较。
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来源期刊
Computers & Structures
Computers & Structures 工程技术-工程:土木
CiteScore
8.80
自引率
6.40%
发文量
122
审稿时长
33 days
期刊介绍: Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.
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