Prediction of electromagnetic wave propagation in three-dimensional dispersive media
Date Issued
2014
Date
2014
Author(s)
Wang, Yu-Chieh
Abstract
An explicit finite-difference scheme for solving the three-dimensional Maxwell''s equations in staggered grids is presented in time domain. The aim of this thesis is to solve the Faraday''s and Ampere''s equations in time domain within the discrete zero-divergence context for the electric and magnetic fields (or Gauss''s law). The local conservation laws in Maxwell''s equations are also numerically preserved all the time using proposed the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme.
Following the method of lines, the spatial derivative terms in the semi-discretized Faraday''s and Ampere''s equations are then properly discretized to get a dispersively very accurate solution. To achieve the goal of getting the best dispersive characteristics, this centered scheme minimizes the difference between the exact and numerical phase velocities with good rates of convergence are demonstrated for the problem. The significant dispersion and anisotropy errors manifested normally in finite difference time domain methods are therefore much reduced. The dual-preserving (symplecticity and dispersion relation equation) wave solver is numerically demonstrated to be efficient for use to get in particular long-term accurate Maxwell''s solutions. The emphasis of this study is also 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 dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell''s solutions for the media of frequency independent and dependent types.
Subjects
馬克斯威爾方程
交錯網格
色散關係
實解相速度和數值相速度
Debye介質
Lorentz介質
Drude介質
Type
thesis
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