An optimal 25-point finite difference scheme for the Helmholtz equation with PML

In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersion, we propose global and refined choice strategies for choosing optimal parameters of the 9-point finite difference scheme. Numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion.