Document Type
Article
Publication Date
3-27-2023
Publication Title
ESAIM: Mathematical Modelling and Numerical Analysis
Volume
57
Issue
2
First page number:
621
Last page number:
644
Abstract
The original Bérenger’s perfectly matched layer (PML) was quite effective in simulating wave propagation problem in unbounded domains. But its stability is very challenging to prove. Later, some equivalent PML models were developed by Bécache and Joly [ESAIM: M2AN 36 (2002) 87–119] and their stabilities were established. Hence studying and developing efficicent numerical methods for solving those equivalent PML models are needed and interesting. Here we propose a novel explicit unconditionally stable finite element scheme to solve an equivalent Bérenger’s PML model. Both the stability and convergence analysis are proved for the proposed scheme. Numerical results justifying the theoretical analysis are presented. We also demonstrate the effectiveness of this PML in simulating wave propagation in the free space. To our best knowledge, this is the first explicit unconditionally stable finite element scheme developed for this PML model.
Keywords
Maxwell’s equations; perfectly matched layer; finite element method
Disciplines
Physical Sciences and Mathematics
File Format
File Size
2200 KB
Language
English
Rights
IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Repository Citation
Huang, Y.,
Li, J.,
Liu, X.
(2023).
Developing and Analyzing an Explicit Unconditionally Stable Finite Element Scheme for an Equivalent Bérenger’s Pml Model.
ESAIM: Mathematical Modelling and Numerical Analysis, 57(2),
621-644.
http://dx.doi.org/10.1051/m2an/2022086
