Speaker: Prof. Honglin Liao

Time: 11:15-12:15, 18 May 2022 (Wednesday) (Beijing time)

Venue:A103,Lijiao Building

Tencent Meeting ID: 170-677-522


Abstract

We address the positive definiteness of discrete time-fractional derivatives, which is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models.  A novel technique is proposed to estimate the minimum eigenvalue of discrete convolution kernels generated by the nonuniform L1, half-grid based L1 and time-averaged L1 formulas of the fractional Caputo's derivative. The main discrete tools are the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Certain variational energy dissipation laws at discrete levels of the variable-step L1-type methods are then established for time-fractional Cahn-Hilliard model. They are shown to be asymptotically compatible, in the fractional order limit , with the associated energy dissipation law for the classical Cahn-Hilliard equation. Numerical examples together with an adaptive time-stepping procedure are provided to demonstrate the effectiveness of the proposed methods.


About Prof. Liao

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年在东南大学数学系获理学博士学位,2001-2017年任教于原解放军理工大学理学院。学术研究方向为偏微分积分方程数值解,目前主要关注线性和非线性偏微分方程的时间变步长离散与时间自适应算法,在Math Comp,SIAM J Numer Anal, SIAM J Sci Comput,IMA J Numer Anal,J Comput Phys, Sci China Math 等国内外专业期刊上发表学术研究论文三十余篇。