A fast regularized boundary integral method for practical acoustic problems

Z. Y. Qian, Z. D. Han, S. N. Atluri

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


To predict the sound field in an acoustic problem, the well-known non-uniqueness problem has to be solved. In a departure from the common approaches used in the prior literature, the weak-form of the Helmholtz differential equation, in conjunction with vector test-functions, is utilized as the basis, in order to directly derive non-hyper-singular boundary integral equations for the velocity potential ø, as well as its gradients q. Both ø-BIE and q-BIE are fully regularized to achieve weak singularities at the boundary [i.e., containing singularities of O(r-1)]. Collocation-based boundary-element numerical approaches [denoted as BEM-R-ø-BIE, and BEM-R-q-BIE] are implemented to solve these. To overcome the drawback of fully populated system matrices in BEM, the fast multipole method is applied, and denoted here as FMM-BEM. The computational costs of FMM-BEM are at the scale of O(2nN), which make it much faster than the matrix based operation, and suitable for large practical problems of acoustics.

Original languageEnglish
Pages (from-to)463-484
Number of pages22
JournalCMES - Computer Modeling in Engineering and Sciences
Issue number6
StatePublished - 2013


  • Boundary integral equations
  • Fast multilevel multipole algorithm


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