New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes
Year: 2021
Author: Xixian Bai, Hongxing Rui
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1355–1383
Abstract
In this paper, several new energy identities of metamaterial Maxwell's equations with the perfectly electric conducting (PEC) boundary condition are proposed and proved. These new energy identities are different from the Poynting theorem. By using these new energy identities, it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete $L^2$ and $H^1$ norms when the Courant-Friedrichs-Lewy (CFL) condition is satisfied. Numerical experiments in two-dimension (2D) and 3D are carried out and confirm our analysis, and the superconvergence in the discrete $H^1$ norm is found.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0208
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1355–1383
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Metamaterial Maxwell's equations Yee scheme non-uniform rectangular meshes energy identities stability.