ON DISCRETE ENERGY DISSIPATION OF MAXWELL’S EQUATIONS IN A COLE-COLE DISPERSIVE MEDIUM  

作　　者：Baoli Yin Yang Liu Hong Li Zhimin Zhang 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China [2]Beijing Computational Science Research Center,Beijing 100193,China [3]Department of Mathematics,Wayne State University,Detroit,MI 48202,USA

出　　处：《Journal of Computational Mathematics》2023年第5期980-1002,共23页计算数学（英文）

基　　金：supported in part by the Grant No.NSFC 12201322;supported in part by Grant No.NSFC 12061053;supported in part by the Grant Nos.NSFC 12161063 and the NSF of Inner Mongolia 2021MS01018;supported in part by Grant Nos.NSFC 11871092 and NSAF U1930402.

摘　　要：A simple criterion is studied for the first time for identifying the discrete energy dissipation of the Crank-Nicolson scheme for Maxwell’s equations in a Cole-Cole dispersive medium.Several numerical formulas that approximate the time fractional derivatives are investigated based on this criterion,including the L1 formula,the fractional BDF-2,and the shifted fractional trapezoidal rule(SFTR).Detailed error analysis is provided within the framework of time domain mixed finite element methods for smooth solutions.The convergence results and discrete energy dissipation law are confirmed by numerical tests.For nonsmooth solutions,the method SFTR can still maintain the optimal convergence order at a positive time on uniform meshes.Authors believe this is the first appearance that a second-order time-stepping method can restore the optimal convergence rate for Maxwell’s equations in a Cole-Cole dispersive medium regardless of the initial singularity of the solution.

关 键 词：Discrete energy dissipation Crank-Nicolson scheme Maxwell’s equations Shifted fractional trapezoidal rule Mixed finite element methods 

分 类 号：O24[理学—计算数学]