Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium

被引：13

作者：

Bai, Xixian ^{[1
]}

Wang, Shuang ^{[1
]}

Rui, Hongxing ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 93卷

基金：

中国国家自然科学基金;

关键词：

Maxwell's equations; Finite-Difference Time-Domain; Energy stability; Error estimate; Numerical experiments; FDTD SCHEME; WAVE-PROPAGATION;

D O I：

10.1016/j.camwa.2021.04.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two efficient numerical schemes based on L1 formula and Finite-Difference Time-Domain (FDTD) method are constructed for Maxwell's equations in a Cole-Cole dispersive medium. The temporal discretizations are built upon the leap-frog method and Crank-Nicolson method, respectively. We carry out the energy stability and error analysis rigorously by the energy method. Both schemes have been proved convergence with order O((Delta t)(2-alpha) + (Delta x)(2) + (Delta y)(2)), where Delta t, Delta x, Delta y are respectively the step sizes in time, space in x-and y-direction. The parameter a is a measure of the dispersion broadening. Numerical experiments are performed to confirm our theoretical analysis.

引用

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页码：230 / 252

页数：23

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