21-point Finite-difference Modeling for the Helmholtz Equation

Abstract

In this paper, we propose a 21-point finite-difference method for solving numerically the Helmholtz equation in 2-dimensional domain, which is a second order scheme. To discretize the Laplacian and the term of zeroth order, a weighted derivative and linear combination of the 21 points are employed respectively, with the weight parameters are determined by minimizing the numerical dispersion. Numerical simulations show that the method is more efficiency than 9-point schemes.