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On energy dissipation theory and numerical stability for time-fractional phase field equations

2019/05/09 10:52  点击:[]

报告人:周 涛(中国科学院数学与系统科学研究院)


日  期:2019年5月12


时  间:上午9:30


地  点:理科楼 LA106


摘  要:For the time-fractional phase field models, the corresponding energy dissipation law has not been well studied on both the continuous and the discrete levels. In this talk, we shall address this open issue. More precisely, we prove for the first time that the time-fractional phase field models indeed admit an energy dissipation law of an integral type. In the discrete level, we propose a class of finite difference schemes that can inherit the theoretical energy stability. Our discussion covers the time-fractional gradient systems, including the time-fractional Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional molecular beam epitaxy models. Numerical examples are presented to confirm the theoretical results. Moreover, a numerical study of the coarsening rate of random initial states depending on the fractional parameter $\alpha$ reveals that there are several coarsening stages for both the time-fractional Cahn-Hilliard equation and the time-fractional molecular beam epitaxy model, while there exists a $-\alpha/3$ power law coarsening stage. This is joint work with Prof. Tao Tang and Prof. Haijun Yu


报告人简介周涛,中国科学院数学与系统科学研究院。2011年博士毕业于中国科学院数学与系统科学研究院。曾于瑞士洛联邦理工大学从事博士后研究。主要研究方向为不确定性量化、随机计算方法以及高维逼近算法等。2016年获中国工业与应用数学学会青年科技奖,2017年获中科院数学与系统科学研究院“陈景润未来之星”称号,并获中科院数学与系统科学研究院“2017年十大科研进展”,2018年获国家自然科学基金委“优秀青年科学基金”资助。2017年起担任国际不确定性量化期刊(International Journal for UQ)副总编(Associate Editor in Chief)。同时担任Commun. Comput. Phys. 和Numerical Mathematics: TMA 两国际期刊编委,2018年起任国际期刊East Asian J. Appl. Math.执行主编(Managing Editor)。2018年起担任国防科工委科学挑战专题领域一“复杂系统模型不确定性评定方法”首席科学家。


学院联系人:王 坤


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