A fourth-order optimal finite difference scheme for the Helmholtz equation with PML. (15th September 2019)

• Record Type: Journal Article
• Authors: Dastour, Hatef; Liao, Wenyuan
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 6(2019)
• Page Start: 2147
• Page End: 2165
• Publication Date: 2019-09-15
• Subjects: Helmholtz equation -- PML -- Optimal finite difference scheme -- Numerical dispersion; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.05.004
• Languages: English
• ISSNs: 0898-1221

Abstract

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.