4.5 Article

New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes

Journal

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
Volume 13, Issue 6, Pages 1355-1383

Publisher

GLOBAL SCIENCE PRESS
DOI: 10.4208/aamm.OA-2020-0208

Keywords

Metamaterial Maxwell's equations; Yee scheme; non-uniform rectangular meshes; energy identities; stability

Funding

  1. National Natural Science Foundation of China [11671233]
  2. Shandong Provincial Science and Technology Development Program [2018GGX101036]

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This paper introduces new energy identities for metamaterial Maxwell's equations with PEC boundary conditions, different from the Poynting theorem. It is proved that the Yee scheme remains stable on non-uniform rectangular meshes when the CFL condition is met. Numerical experiments confirm the analysis and reveal superconvergence in the discrete H-1 norm.
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 twodimension (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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