Journals
Resources
About Us
Open Access

Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media

Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

​Puttha Sakkaplangkul

Vrushali A. Bokil