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

Haifeng Gao, Toshiro Matsumoto, Toru Takahashi, Hiroshi Isakari

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)914-923
Number of pages10
JournalEngineering Analysis with Boundary Elements
Issue number6
Publication statusPublished - 2013
Externally publishedYes


  • Acoustic
  • Boundary element method
  • Burton-Miller's method
  • Eigenvalues
  • The block SS method

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics


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