Development of a symplectic scheme with optimized numerical dispersion-relation equation to solve Maxwell's equations in dispersive media
Date Issued
2012
Date
2012
Author(s)
Chung, Rih-Yang
Abstract
In this paper an explicit nite-di erence scheme is developed in staggered grids for solving the Maxwell''s equations in time domain. It is aimed to preserve the discrete zero-divergence condition in the electrical and magnetic
elds and conserve some inherent laws in non-dispersive media all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme. The spatial derivative terms in the resulting semi-discretized
Faraday''s and Ampere''s equations are approximated to get an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumber for the Maxwell''s equations in a domain of two space dimensions. To achieve the goal of getting the best dispersive characteristics, a fourth-order accurate space centered scheme with the ability of minimizing the di erence between the exact and numerical dispersion relation equations is proposed. The emphasis of this study is placed on the accurate modelling of EM waves in the dispersive media of the Debye, Lorentz and Drude types. Through the computational exercises, the proposed dualpreserving solver is computationally demonstrated to be e cient for use to
predict the long-term accurate Maxwell''s solutions for the media of frequency independent and dependent types.
Subjects
Debye
Lorentz
Drude
dual-preserving solver
dispersion relation equation
frequency dependent
Type
thesis
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