A fourth-order optimal finite difference scheme for the Helmholtz equation with PML
Published in Computers & Mathematics with Applications, 2019
Recommended citation: Dastour H. and Liao, W. (2019). A fourth-order optimal finite difference scheme for the Helmholtz equation with PML. Computers & Mathematics with Applications, 78(6):2147--2165. [IF: 2.9; IF Quartile: Q1] https://www.sciencedirect.com/science/article/pii/S0898122119302676
Abstract:
In this paper, 17-point and 25-point finite difference (FD) schemes for the Helmholtz equation with perfectly matched layer (PML) in the two-dimensional domain are presented. It is shown that the 17-point FD scheme is inconsistent in the presence of PML; however, the 25-point FD scheme is pointwise consistent. An error analysis for the numerical approximation of the exact wavenumber is also presented. We present the global and refined 25-point finite difference schemes based on minimizing the numerical dispersion. Numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion.