### Abstract

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 language | English |
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Pages (from-to) | 463-484 |

Number of pages | 22 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 91 |

Issue number | 6 |

State | Published - 2013 |

### Keywords

- Boundary integral equations
- Fast multilevel multipole algorithm

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## Cite this

*CMES - Computer Modeling in Engineering and Sciences*,

*91*(6), 463-484.