Gopalaswamy B., Rice H.

Abstract: Modelling sound propagation over large domains presents severe challenges with respect to computational requirements. In general, direct solutions of system equations resulting from the full field discretization of many three-dimensional problems of practical interest cannot be attempted. The present study proposes the construction of a suitable preconditioner for iteratively solving a 3D Helmholtz equation. The discretization is done using a Wave Based Finite Difference scheme known as the Wave Expansion Method (WEM). The WEM requires only 2-3 nodes per wavelength to obtain accurate solutions which offers a potential for major improvement in efficiency compares to conventional techniques such as the Finite Element/Finite Difference approaches which require around 8-10 nodes per wavelength. Iterative solution of any Helmholtz system model requires a careful preconditioning strategy in order to ensure convergence. The preconditioners here are obtained by an incomplete factorization of the stiffness matrix. A suitable preconditioner is constructed by choosing an appropriate pivoting threshold. The level at which the threshold is set is determined by the available memory resources. Results are presented for box-shaped domains of varying problem sizes and a range of frequencies. This preconditioning strategy has been found to work well with large problem sizes and with nodal densities as low as 3 per wavelength. The preconditioner has also been shown to work well with reflective and radiation boundary conditions.