| 边界元奇异与近奇异数值积分方法及其应用于大规模声学问题 |
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| 引用本文： | 龚家元, 安俊英, 马力, 徐海亭. 边界元奇异与近奇异数值积分方法及其应用于大规模声学问题[J]. 声学学报, 2016, 41(5): 768-775. DOI: 10.15949/j.cnki.0371-0025.2016.05.029 |
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| 作者姓名： | 龚家元 安俊英 马力 徐海亭 |
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| 作者单位： | 1 中国科学院声学研究所北海研究站 青岛 266023; |
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| 基金项目： | 国家自然科学基金项目(11304344,11404364)、中国科学院声学研究所青年人才领域前沿和知识创新工程重要方向项目资助 |
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| 摘 要： | 提出了综合处理Burton-Miller方法所导致的奇异积分与近奇异积分问题的数值求积方法,以此改进了基于常量元素的常规边界元和低频快速多极边界元方法。对于奇异积分问题,利用Hadamard有限积分方法进行解决;对于近奇异积分问题,则采用极坐标变换法和PART方法(Projection and Angular&;Radial Transformation)进行克服。与解析解和LMS Virtual.Lab商业软件的结果比较验证了方法的正确性,并对比分析了奇异积分与近奇异积分对计算精度的影响。采用低频快速多极子方法以加速常规边界元法的计算效率,计算分析了计算复杂度,并成功实现了34万自由度大规模问题的计算。结果表明,近奇异积分问题主要由超奇异核函数引起,对计算精度的影响不容忽略;快速多极边界元法的精度与常规边界元法一致,但计算复杂度要远低于后者。
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| 收稿时间： | 2015-12-15 |
| 修稿时间： | 2016-03-31 |
Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems |
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| GONG Jiayuan, AN Junying, MA Li, XU Haiting. Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems[J]. ACTA ACUSTICA, 2016, 41(5): 768-775. DOI: 10.15949/j.cnki.0371-0025.2016.05.029 |
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| Authors: | GONG Jiayuan AN Junying MA Li XU Haiting |
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| Affiliation: | 1 Qingdao Branch, Institute of Acoustics, Chinese Academy of Sciences Qingdao 266023;2 School of Electrical and Information Engineering, Hubei University of Automotive Technology Shiyan 442002;3 Key Laboratory of Underwater Acoustic Environment, Institute of Acoustics, Chinese Academy of Sciences Beijing 100190 |
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| Abstract: | The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEM (boundary element method) for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by both the simple method of polar transformation and the more complex method of PART (Projection and Angular & Radial Transformation). The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem of results show that, the near singularity is primarily introduced about 340,000 freedoms is implemented successfully. The by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower |
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