A modified singular boundary method for three-dimensional high frequency acoustic wave problems

The main purpose of this article is to propose a modified singular boundary method using the modified fundamental solution of Helmholtz equation for simulation of three-dimensional high frequency acoustic wave problems. Compared with the standard second-order discretization methods which usually need to place more than 10-12 grid points in one wavelength per direction, the newly proposed modified singular boundary method only needs 2-3 source points in one wavelength of each direction to produce the accurate solutions with relative error around 1E − 3 level which satisfies most application requirements. It is observed that the present algorithm has similar condition number to the boundary element method and can hereby be solved efficiently by the iterative solver. By adopting the range restricted generalized minimal residual algorithm iterative solver, numerical experiments with 194,400 source points have successfully been achieved on a single laptop for three-dimensional high frequency acoustic wave problems with up to wavenumber 440.