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Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes

Jichun Li University of Nevada Las Vegas Sidney Shields University of Nevada Las Vegas

Numerical Analysis and Scientific Computing mathscidoc:1702.25001

Numerische Mathematik, 134, 741–781, 2016.12
Since the development of Yee scheme back in 1966, it has become one of the most popular simulation tools for modeling electromagnetic wave propagation in various situations.However, its rigorous error analysis on nonuniform rectangular type gridswas carried out until 1994 by Monk and Süli. They showed that theYee scheme is still second-order convergent on a nonuniform mesh even though the local truncation error is only of first order. In this paper, we extend their results to Maxwell’s equations in metamaterials by a simpler proof, and show the second-order superconvergence in space for the trueYee scheme instead of the only semi-discrete form discussed in Monk and Süli’s original work. Numerical results supporting our analysis are presented.
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@inproceedings{jichun2016superconvergence,
  title={Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes},
  author={Jichun Li, and Sidney Shields},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205124418191554164},
  booktitle={Numerische Mathematik},
  volume={134},
  pages={741–781},
  year={2016},
}
Jichun Li, and Sidney Shields. Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes. 2016. Vol. 134. In Numerische Mathematik. pp.741–781. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205124418191554164.
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