An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

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• 作者：Chang-Jun Zheng^a ; ^{cjzheng@hfut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hai-Feng Gao^b ; ^{gao_h@wzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Lei Du^c ; ^{dulei@dlut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hai-Bo Chen^d ; ^{hbchen@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Chuanzeng Zhang^e ; ^{c.zhang@uni-siegen.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Acoustic eigenvalue analysis ; Boundary element method ; Wideband fast multipole method ; Contour integral method ; Fictitious eigenvalues ; Coupling parameter
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：677-699
• 全文大小：5551 K

文摘

An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR(s)$\mathrm{IDR}(s)$ solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton–Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton–Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α=i/k$\alpha =\mathrm{i}/k$ is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.