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Volume 11, Issue 4
Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media

V. A. Bokil & N. L. Gibson

Int. J. Numer. Anal. Mod., 11 (2014), pp. 657-687.

Published online: 2014-11

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  • Abstract

We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The energy decay results are then used to prove the convergence of the Yee schemes for the dispersive models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete mesh. Numerical simulations are provided to illustrate the theoretical results.

  • Keywords

Maxwell's equations, Debye, Lorentz dispersive materials, Yee, FDTD method, energy decay, convergence analysis.

  • AMS Subject Headings

65M06, 65M12, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-657, author = {Bokil , V. A. and Gibson , N. L.}, title = {Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {657--687}, abstract = {

We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The energy decay results are then used to prove the convergence of the Yee schemes for the dispersive models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete mesh. Numerical simulations are provided to illustrate the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/546.html} }
TY - JOUR T1 - Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media AU - Bokil , V. A. AU - Gibson , N. L. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 657 EP - 687 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/546.html KW - Maxwell's equations, Debye, Lorentz dispersive materials, Yee, FDTD method, energy decay, convergence analysis. AB -

We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The energy decay results are then used to prove the convergence of the Yee schemes for the dispersive models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete mesh. Numerical simulations are provided to illustrate the theoretical results.

Bokil , V. A. and Gibson , N. L.. (2014). Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media. International Journal of Numerical Analysis and Modeling. 11 (4). 657-687. doi:
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