☆ 4.7 Article

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

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2021)

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

Volume 93, Issue -, Pages 230-252

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

DOI: 10.1016/j.camwa.2021.04.015

Keywords

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

Categories

Mathematics, Applied

Funding

National Natural Science Foundation of China [11671233]
Shandong Provincial Key Research and Development Project Grant [2018GGX101036]
Shandong Provincial Natural Science Foundation Grant [ZR2019PA021]

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Abstract

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. By rigorously carrying out energy stability and error analysis using the energy method, it is proven that both schemes converge with a certain order. Numerical experiments are performed to confirm the theoretical analysis.

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.

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