Development and Analysis of Both Finite Element and Fourth-Order in Space Finite Difference Methods for an Equivalent Berenger's PML Model
Document Type
Article
Publication Date
11-29-2019
Publication Title
Journal of Computational Physics
Volume
405
First page number:
1
Last page number:
20
Abstract
This paper deals with an equivalent Berenger's Perfectly Matched Layer (PML) model. We first develop a finite element scheme using edge elements to solve this model. We prove a discrete stability of this method, which inherits the stability obtained in the continuous case. Then we propose a fourth-order in space finite difference scheme for solving this PML model. Numerical stability similar to the continuous stability and the optimal error estimate are established for the difference scheme. Here only second order time discretizations are considered for both schemes. Finally, numerical results are presented to justify our analysis and demonstrate the effectiveness of this PML model for absorbing impinging waves.
Keywords
Maxwell's equations; Perfectly Matched Layer; Finite difference method; Finite element method; Edge elements
Disciplines
Mathematics | Physical Sciences and Mathematics
Language
English
Repository Citation
Huang, Y.,
Chen, M.,
Li, J.
(2019).
Development and Analysis of Both Finite Element and Fourth-Order in Space Finite Difference Methods for an Equivalent Berenger's PML Model.
Journal of Computational Physics, 405
1-20.
http://dx.doi.org/10.1016/j.jcp.2019.109154