@Article{cmes.2013.091.463,
AUTHOR = {Z.Y. Qian, Z.D. Han, S.N. Atluri},
TITLE = {A Fast Regularized Boundary Integral Method for Practical Acoustic Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {91},
YEAR = {2013},
NUMBER = {6},
PAGES = {463--484},
URL = {http://www.techscience.com/CMES/v91n6/26928},
ISSN = {1526-1506},
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 <i>q</i>;. Both ∅-BIE and <i>q</i>-BIE are fully regularized to achieve weak singularities at the boundary [i.e., containing singularities of <i>O(r<sup>-1</sup>)</i>]. Collocation-based boundary-element numerical approaches [denoted as BEM-R-∅-BIE, and BEM-R-<i>q</i>-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(<i>2nN</i>), which make it much faster than the matrix based operation, and suitable for large practical problems of acoustics.},
DOI = {10.3970/cmes.2013.091.463}
}