{"title":"A frequency-independent absorption function surrogate for perfectly matched layer in exterior acoustics","authors":"","doi":"10.1016/j.compstruc.2024.107569","DOIUrl":null,"url":null,"abstract":"<div><div>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, <em>e.g.</em> 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.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045794924002980","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.