Year: 2014
Author: V. A. Bokil, N. L. Gibson
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-546
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 657–687
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Maxwell's equations Debye Lorentz dispersive materials Yee FDTD method energy decay convergence analysis.