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      南京航空航天大学廖洪林教授学术报告预告

      发布时间:2023-11-19 17:56 作者:文/任金城 点击:[]

      报告题目:AC-preserving energy of variable-step fractional BDF2 scheme for time-fractional Cahn-Hilliard model

      报告人:廖洪林

      报告摘要:A new discrete energy dissipation law of the variable-step fractional BDF2 (second-order backward differentiation formula) scheme is established for time-fractional Cahn-Hilliard model under a weak step-ratio constraint. We propose a novel discrete gradient structure by a local-nonlocal splitting technique, that is, the fractional BDF2 formula is split into a local part analogue to the two-step backward differentiation formula of the first derivative and a nonlocal part analogue to the L1-type formula of the Caputo's derivative. More interestingly, in the sense of the limit $\alpha\rightarrow1^-$, the discrete energy and the corresponding energy dissipation law are asymptotically compatible with the associated discrete energy and the energy dissipation law of the variable-step BDF2 method for the classical Cahn-Hilliard equation, respectively. Numerical examples with an adaptive stepping procedure are provided to demonstrate the accuracy and the effectiveness of our proposed method.

      报告人简介:廖洪林,应用数学博士,2018年至今任教于南京航空航天大学数学学院。2001年在原解放军理工大学获理学硕士学位,2010年在东南大学获理学博士学位,2001-2017年任教于原解放军理工大学。学术研究方向为微分方程数值解,目前主要关注相场以及多相流模型的时间变步长离散与自适应算法, Math CompSIAM J Numer Anal, SIAM J Sci ComputJ Comput Phys, IMA J Numer AnalSci China Math等国内外专业期刊上发表学术研究论文四十余篇。

      时间:20231124日下午15

      地点:教科楼B863

      邀请人:任金城

      主办单位:william威廉亚洲官方


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