Year: 2021
Author: Puttha Sakkaplangkul, Vrushali A. Bokil
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 524–568
Abstract
In this paper, we develop and analyze finite difference methods for the 3D Maxwell's equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19113
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 524–568
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 45
Keywords: Maxwell's equations Debye Lorentz cold plasma dispersive media Yee scheme FDTD method energy decay convergence analysis.