TY - EJOU
AU - Han, Z.Y. Qian, Z.D.
AU - Atluri, S.N.
TI - A Fast Regularized Boundary Integral Method for Practical Acoustic Problems
T2 - Computer Modeling in Engineering \& Sciences
PY - 2013
VL - 91
IS - 6
SN - 1526-1506
AB - 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.
KW - Boundary integral equations
KW - Fast multilevel multipole algorithm
DO - 10.3970/cmes.2013.091.463