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, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，J Comput Phys, IMA J Numer Anal，Sci 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：2023年11月24日下午15点
地点：教科楼B座863
邀请人：任金城
主办单位：数学与信息科学学院
