Developing finite element methods for maxwell's equations in a cole-cole dispersive medium

Jichun Li, Yunqing Huang, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

44 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)3153-3174
Number of pages22
JournalSIAM Journal on Scientific Computing
Volume33
Issue number6
DOIs
Publication statusPublished - 1 Dec 2011

Keywords

  • Cole-Cole model
  • Dispersive medium
  • Finite element method
  • Maxwell's equations

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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