Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell's Equations in Dispersive Media

Authors:
Jichun Li
Affiliations:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China 411105 and Department of Mathematical Sciences, University of Nevada Las Vegas, ...
Venue:
Journal of Scientific Computing
Year:
2011

Citing 8
Cited 2

Global superconvergence for Maxwell's equations

Mathematics of Computation
Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients

SIAM Journal on Numerical Analysis
Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations

SIAM Journal on Numerical Analysis
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

Journal of Computational Physics
Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

Journal of Computational Physics
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

SIAM Journal on Numerical Analysis
Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma

Journal of Scientific Computing
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Developing Finite Element Methods for Maxwell's Equations in a Cole-Cole Dispersive Medium

SIAM Journal on Scientific Computing
Operator splitting methods for Maxwell's equations in dispersive media with orientational polarization

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we consider the time dependent Maxwell's equations resulting from dispersive medium models. First, the stability and Gauss's law are proved for all three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Then leap-frog mixed finite element methods are developed for these three models. Optimal error estimates are proved for all three models solved by the lowest-order Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also. Numerical results confirming the analysis are presented.