A dispersion minimizing compact finite difference scheme for the 2D Helmholtz equation

In this paper, we present a dispersion minimizing compact finite difference scheme for solving the 2D Helmholtz equation, which is a fourth-order scheme. The error between the numerical wavenumber and the exact wavenumber is analyzed, and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters.