A fast regularized boundary integral method for practical acoustic problems

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.