Mathematical Analysis of Ziolkowski's PML Model With Application for Wave Propagation in Metamaterials
Document Type
Article
Publication Date
3-1-2020
Publication Title
Journal of Computational and Applied Mathematics
Volume
366
Abstract
© 2019 Elsevier B.V. In this paper we investigate one Perfectly Matched Layer (PML) model proposed by Ziolkowski in 1999. Various schemes for solving this PML model have been developed and have been shown to be effective in absorbing outgoing waves when the wave propagation in unbounded domain problem is reduced to a bounded domain problem. However, a rigorous analysis of this model is lacking. In this paper we establish the stability of this PML model and propose a fully-discrete finite element scheme to solve this model with edge elements. Discrete stability and optimal error estimate of this scheme are proved. Numerical results justifying the analysis and demonstrating the effectiveness of this PML model are presented.
Keywords
Edge element; Finite element method; Maxwell's equations; Metamaterial; Perfectly matched layers
Disciplines
Applied Mathematics
Language
English
Repository Citation
Huang, Y.,
Li, J.,
Fang, Z.
(2020).
Mathematical Analysis of Ziolkowski's PML Model With Application for Wave Propagation in Metamaterials.
Journal of Computational and Applied Mathematics, 366
http://dx.doi.org/10.1016/j.cam.2019.112434