用等几何边界元法解决声散射问题

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-07-01 DOI:10.1007/s00366-024-02013-y
Jürgen Dölz, Helmut Harbrecht, Michael Multerer
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引用次数: 0

摘要

我们通过等几何边界积分方程法解决声散射问题。为了避免虚假模式,我们应用了声硬散射体或声软散射体的组合场积分方程。这些积分方程采用 Galerkin 方法进行离散化处理,尤其能对超正弦积分算子进行正确的数学正则化处理。为了避开密集的系统矩阵,我们采用了等几何嵌入式快速多极法,该方法基于在参考域而非空间对所考虑的核函数进行插值。为了克服在评估点较多的情况下势能评估成本过高的问题,我们还采用了在空间进行插值的快速多极法来加速势能评估。这样就产生了一种频率稳定的算法,其规模与自由度和电位点的数量基本成线性关系。我们进行的数值实验表明了该方法的可行性和性能。
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Solving acoustic scattering problems by the isogeometric boundary element method

We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These integral equations are discretized by Galerkin’s method, which especially enables the mathematically correct regularization of the hypersingular integral operator. In order to circumvent densely populated system matrices, we employ the isogeometric embedded fast multipole method, which is based on interpolation of the kernel function under consideration on the reference domain, rather than in space. To overcome the prohibitive cost of the potential evaluation in case of many evaluation points, we also accelerate the potential evaluation by a fast multipole method which interpolates in space. The result is a frequency stable algorithm that scales essentially linear in the number of degrees of freedom and potential points. Numerical experiments are performed which show the feasibility and the performance of the approach.

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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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