Diagonal form fast multipole singular boundary method applied to the solution of high‐frequency acoustic radiation and scattering

The singular boundary method (SBM) is a recent strong‐form boundary collocation method that uses a linear combination of the fundamental solution of the governing equation to approximate the field variables. Because of its full interpolation matrix, the SBM solution encounters the high computational complexity and storage requirement that limit its applications to large‐scale engineering problems. This paper presents a way to overcome this drawback by introducing the diagonal form fast multipole method. A diagonal form fast multipole singular boundary method is then developed to reduce the computational operations of the SBM with direct solvers from O(N3) to O(NlogN), where N is the number of unknowns. The proposed method works well for acoustic radiation and scattering with nondimensional wave number kD<110 (k is the wave number and D the maximum diameter of the computational domain). Several numerical experiments are provided to show the efficiency and accuracy of the present strategy, including the radiation from a nuclear submarine and the scattering from an airplane. The numerical results clearly demonstrate that the present diagonal form fast multipole singular boundary method breaks the limitations of the SBM and successfully simulates the large‐scale acoustic problems with more than one million unknowns on a desktop computer. Copyright © 2016 John Wiley & Sons, Ltd.