{"title":"Free-Form Deformation as a non-invasive, discrete unfitted domain method: Application to the time-harmonic acoustic response of a saxophone","authors":"","doi":"10.1016/j.cma.2024.117345","DOIUrl":null,"url":null,"abstract":"<div><p>The Finite Element method, widely used for solving Partial Differential Equations, may result in suboptimal computational costs when computing smooth fields within complex geometries. In such situations, IsoGeometric Analysis often offers improved per degree-of-freedom accuracy but building analysis-suitable representation of complex shapes is generally not obvious. This paper introduces a non-invasive, spline-based fictitious domain method using Free-Form Deformation to efficiently solve the Helmholtz equation in complex domains, such as in musical instruments. By immersing a fine FE mesh into a simple B-spline box, the approximation subspace size is significantly reduced without compromising accuracy. Accompanied by specific conditioning treatment, the method not only proves to be efficient, but also robust and easy to implement in existing FE software. Applied to an alto saxophone, the method reduces the number of degrees of freedom by over two orders of magnitude and the computation time by more than one compared to standard FE methods with comparable accuracy when compared to experimental tests.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524006005/pdfft?md5=228e33820ead6b3264f1123031aedfbb&pid=1-s2.0-S0045782524006005-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782524006005","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The Finite Element method, widely used for solving Partial Differential Equations, may result in suboptimal computational costs when computing smooth fields within complex geometries. In such situations, IsoGeometric Analysis often offers improved per degree-of-freedom accuracy but building analysis-suitable representation of complex shapes is generally not obvious. This paper introduces a non-invasive, spline-based fictitious domain method using Free-Form Deformation to efficiently solve the Helmholtz equation in complex domains, such as in musical instruments. By immersing a fine FE mesh into a simple B-spline box, the approximation subspace size is significantly reduced without compromising accuracy. Accompanied by specific conditioning treatment, the method not only proves to be efficient, but also robust and easy to implement in existing FE software. Applied to an alto saxophone, the method reduces the number of degrees of freedom by over two orders of magnitude and the computation time by more than one compared to standard FE methods with comparable accuracy when compared to experimental tests.
广泛用于求解偏微分方程的有限元法,在计算复杂几何形状中的平滑场时,可能会导致计算成本过低。在这种情况下,等几何分析法通常能提高单位自由度的精度,但建立适合分析的复杂形状表示通常并不明显。本文介绍了一种非侵入式、基于样条线的虚构域方法,该方法使用自由形态变形来有效求解复杂域中的亥姆霍兹方程,例如乐器中的亥姆霍兹方程。通过将精细的 FE 网格浸入简单的 B-spline 框中,可在不影响精度的情况下显著减小近似子空间的大小。伴随着特定的调节处理,该方法不仅被证明是高效的,而且也是稳健的,易于在现有的 FE 软件中实施。该方法应用于中音萨克斯管,与标准 FE 方法相比,自由度数量减少了两个数量级以上,计算时间减少了一个数量级以上,与实验测试相比,精度相当。
期刊介绍:
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.