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Volume 27, Issue 6
Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations

Nengsheng Fang & Lung-An Ying

DOI: 10.4208/jcm.2009.09-m2808

J. Comp. Math., 27 (2009), pp. 729-747.

Published online: 2009-12

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  • Abstract

We utilize Fourier methods to analyze the stability of the Yee difference schemes for Bérenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.

  • Keywords

Computational electromagnetic, Fourier method, Yee scheme, PML, UPML, Stability.

  • AMS Subject Headings

65M12.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-729, author = {Fang , Nengsheng and Ying , Lung-An}, title = {Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {6}, pages = {729--747}, abstract = {

We utilize Fourier methods to analyze the stability of the Yee difference schemes for Bérenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2808}, url = {http://global-sci.org/intro/article_detail/jcm/8600.html} }
TY - JOUR T1 - Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations AU - Fang , Nengsheng AU - Ying , Lung-An JO - Journal of Computational Mathematics VL - 6 SP - 729 EP - 747 PY - 2009 DA - 2009/12 SN - 27 DO - http://doi.org/10.4208/jcm.2009.09-m2808 UR - https://global-sci.org/intro/article_detail/jcm/8600.html KW - Computational electromagnetic, Fourier method, Yee scheme, PML, UPML, Stability. AB -

We utilize Fourier methods to analyze the stability of the Yee difference schemes for Bérenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.

Nengsheng Fang & Lung-An Ying. (2019). Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations. Journal of Computational Mathematics. 27 (6). 729-747. doi:10.4208/jcm.2009.09-m2808
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