Open Access

ARTICLE

A Fast Regularized Boundary Integral Method for Practical Acoustic Problems

Z.Y. Qian, Z.D. Han¹, S.N. Atluri^{1, 2}

1 Center for Aerospace Research & Education, University of California, Irvine, CA 92612, USA
2 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.

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