An optimal compact sixth-order finite difference scheme for the Helmholtz equation

Abstract

In this paper, we present an optimal compact finite difference scheme for solving the 2D Helmholtz equation. A convergence analysis is given to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, a refined optimization rule for choosing the scheme’s weight parameters is proposed. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters.