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On discrete energy dissipation of Maxwell's equations in a Cole-Cole dispersive Medium
[数学科学学院]  [手机版本]  [扫描分享]  发布时间:2022年6月6日
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报告题目:On discrete energy dissipation of Maxwell's equations in a Cole-Cole dispersive Medium

报告人 刘洋内蒙古大学教授

报告地点:腾讯会议 (会议号180578607

报告时间2022-06-09(周四)13:00-14:30

报告摘要:A simple criterion is studied for the first time for identifying the discrete energy dissipation of the Crank-Nicolson scheme for Maxwells equations in a Cole-Cole dispersive medium. Several numerical formulas that approximate the time fractional derivatives are investigated based on this criterion. 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 Maxwells equations in a Cole-Cole dispersive medium regardless of the initial singularity of the solution.

报告人简介:刘洋,内蒙古大学数学科学学院教授、博士生导师,兼任中国数学会计算数学分会理事、仿真算法专业委员会委员、内蒙古数学会理事、美国《数学评论》评论员等。主要从事微分方程数值解法研究。在JCP、BIT、JSC、International Journal of Heat and Mass Transfer等期刊上发表SCI论文70余篇。主持3项国家自然科学基金。2020年获内蒙古自然科学二等奖、入选2020年度“草原英才”工程青年创新创业人才一层次、入选2021年度自治区“新世纪321人才工程”一层次人选。

 

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