声学中的不确定性分析:扰动法和等几何边界元法

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-07-01 DOI:10.1007/s00366-024-02018-7
Leilei Chen, Haojie Lian, Ruijin Huo, Jing Du, Weisong Liu, Zhuxuan Meng, Stéphane P. A. Bordas
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引用次数: 0

摘要

本研究提出了一种基于(等几何)边界元方法的广义 nth 阶扰动方法,用于三维声散射问题的不确定性分析。本文首次将入射波频率作为随机输入变量,推导出三维声学边界积分方程的 nth 阶泰勒展开。此外,为了避免繁琐的网格划分过程并保持几何精度,我们采用了几何建模中使用的细分曲面基函数来离散广义 nth 阶导数边界积分方程。此外,还引入了快速多极子方法,以加速边界元方法的随机扰动分析。通过给出数值示例,证明了所提出的不确定性量化算法的准确性和高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Uncertainty analysis in acoustics: perturbation methods and isogeometric boundary element methods

This study proposes a generalized nth-order perturbation method based on (isogeometric) boundary element methods for uncertainty analysis in 3D acoustic scattering problems. In this paper, for the first time, we derive nth-order Taylor expansions of 3D acoustic boundary integral equations, taking incident wave frequency as a random input variable. In addition, subdivision surface basis functions used in geometric modeling are employed to discretize the generalized nth-order derivative boundary integral equations, in order to avoid cumbersome meshing procedure and retain geometric accuracy. Moreover, the fast multipole method is introduced to accelerate the stochastic perturbation analysis with boundary element methods. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed uncertainty quantification algorithm.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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