Academic Lecture of College of Cyber Security (No. 31)
Topic: Energy-decaying Runge--Kutta SAV methods for phase field equations
Speaker: Prof. Li Dongfang, Huazhong University of Science and Technology
Date: Thursday, Nov. 14, 2019
Time: 10:30 am
Venue: Room 338, Naihai Building
Abstract: We construct and analyze a class of extrapolated and linearized Runge--Kutta (RK) methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn and Cahn--Hilliard phase field equations, based on the scalar auxiliary variable (SAV) formulation. We prove that the proposed qq-stage RK--SAV methods have qqth-order convergence in time and satisfy a discrete version of the energy decay property. Numerical examples are provided to illustrate the discrete energy decay property and accuracy of the proposed methods.
Introduction to speaker: Prof. Li, a doctoral supervisor and a member of the simulation algorithm professional committee of China Simulation Federation, is mainly engaged in the research in Numerical Methods for Differential Equations, system simulation  and information processing.He was engaged in his postdoctoral research in McGill university in Canada and City university of Hong Kong successively. Up to now, he has published more than 30 papers in several international SCI academic periodicals in computing as the first author or corresponding author. Li has presided over one project of National Natural Science Foundation, one of Youth Fund and one of Postdoctoral Sustentation Fund and participated in a number of projects from National Natural Science Foundation. He has won the award of Academic Newcomer in Huazhong University of Science and Technology and the award of Xiangjiang Scholar.