A fourth-order optimal finite difference scheme for the Helmholtz equation with PML

摘要

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. (C) 2019 Elsevier Ltd. All rights reserved.