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Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

查看全文 作　　者：GONG [1,2]Jiayuan;AN [1]Junying;MA [3]Li;XU [1]Haiting 高影响力作者 机构地区：[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,Hubei Province 442002;[3]Key Laboratory of Underwater Acoustic Environment,Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190高影响力机构 出　　处：《Chinese Journal of Acoustics》索引2017年第36卷第3期,共13页高影响力期刊 基　　金：supported by the National Natural Science Foundation of China(11304344,11404364);the Project of Hubei Provincial Department of Education(D20141803);the Natural Science Foundation of Hubei Province(2014CFB378);the Doctoral Scientific Research Foundation of Hubei University of Automotive Technology(BK201604) 摘　　要：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 BEMs(boundary element methods) 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 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,whose degree of freedoms is about 340,000,is implemented successfully.The results show that,the near singularity is primarily introduced 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. 关 键 词：奇异积分 边界元法 声学问题 数值积分 HADAMARD 计算精度 应用 Burton
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