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Developing finite element methods for maxwell’s equations in a cole–cole dispersive medium

Jichun Li University of Nevada Las Vegas

Numerical Analysis and Scientific Computing mathscidoc:1702.25017

SIAM Journal on Scientific Computing, 33, (6), 3153–3174, 2011
In this paper, we consider the time-dependent Maxwell’s equations when Cole–Cole dispersive medium is involved. The Cole–Cole model contains a fractional time derivative term, which couples with the standard Maxwell’s equations in free space and creates some challenges in developing and analyzing time-domain finite element methods for solving this model as mentioned in our earlier work [J. Li, J. Sci. Comput., 47 (2001), pp. 1–26]. By adopting some techniques developed for the fractional diffusion equations [V.J. Ervin, N. Heuer, and J.P. Roop, SIAM J. Numer. Anal., 45 (2007), pp. 572–591], [Y. Lin and C. Xu, J. Comput. Phys., 225 (2007), pp. 1533–1552], [F. Liu, P. Zhuang, V. Anh, I. Turner, and K. Burrage, Appl. Math. Comput., 191 (2007), pp. 12–20], we propose two fully discrete mixed finite element schemes for the Cole–Cole model. Numerical stability and optimal error estimates are proved for both schemes. The proposed algorithms are implemented and detailed numerical results are provided to justify our theoretical analysis.
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@inproceedings{jichun2011developing,
  title={DEVELOPING FINITE ELEMENT METHODS FOR MAXWELL’S EQUATIONS IN A COLE–COLE DISPERSIVE MEDIUM},
  author={Jichun Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205133518362851180},
  booktitle={SIAM Journal on Scientific Computing},
  volume={33},
  number={6},
  pages={3153–3174},
  year={2011},
}
Jichun Li. DEVELOPING FINITE ELEMENT METHODS FOR MAXWELL’S EQUATIONS IN A COLE–COLE DISPERSIVE MEDIUM. 2011. Vol. 33. In SIAM Journal on Scientific Computing. pp.3153–3174. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205133518362851180.
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