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A Fast Regularized Boundary Integral Method for Practical Acoustic Problems

Z.Y. Qian, Z.D. Han1, S.N. Atluri1, 2
Center for Aerospace Research & Education, University of California, Irvine, CA 92612, USA
Distinguished Visiting Professor of Multi-Disciplinary Engineering and Computer Science, King Abdul Aziz University, Saudi Arabia

Computer Modeling in Engineering & Sciences 2013, 91(6), 463-484. https://doi.org/10.3970/cmes.2013.091.463

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 ∅, as well as its gradients q;. Both ∅-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-∅-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.

Keywords

Boundary integral equations, Fast multilevel multipole algorithm

Cite This Article

Qian,, Z., Atluri, S. (2013). A Fast Regularized Boundary Integral Method for Practical Acoustic Problems. CMES-Computer Modeling in Engineering & Sciences, 91(6), 463–484.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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