Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method

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• 作者：Haifeng Gao ; ^{gao_h@nuem.nagoya-u.ac.jp} ; ^{gaohaifeng8899@gmail.com} ; Toshiro Matsumoto ^{t.matsumoto@nuem.nagoya-u.ac.jp} ; Toru Takahashi ^{ttaka@nuem.nagoya-u.ac.jp} ; Hiroshi Isakari ^{isakari@nuem.nagoya-u.ac.jp}
• 关键词：Eigenvalues ; Acoustic ; The block SS method ; Boundary element method ; Burton&ndash ; Miller's method
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：37
• 期：6
• 页码：914-923
• 全文大小：6665 K

文摘

This paper presents accurate numerical solutions for nonlinear eigenvalue analysis of three-dimensional acoustic cavities by boundary element method (BEM). To solve the nonlinear eigenvalue problem (NEP) formulated by BEM, we employ a contour integral method, called block Sakurai-Sugiura (SS) method, by which the NEP is converted to a standard linear eigenvalue problem and the dimension of eigenspace is reduced. The block version adopted in present work can also extract eigenvalues whose multiplicity is larger than one, but for the complex connected region which includes a internal closed boundary, the methodology yields fictitious eigenvalues. The application of the technique is demonstrated through the eigenvalue calculation of sphere with unique homogenous boundary conditions, cube with mixed boundary conditions and a complex connected region formed by cubic boundary and spherical boundary, however, the fictitious eigenvalues can be identified by Burton-Miller's method. These numerical results are supported by appropriate convergence study and comparisons with close form.