题目：Discrete maximum principle of exponential time differencing schemes for nonlocal Allen-Cahn equations
报告人：乔中华 博士
时间：2018年3月31日15：30-16：30
地点：数学楼202
报告人简介：
乔中华博士于2006年在香港浸会大学获得博士学位，现在是香港理工大学应用数学系副教授。在2011年12月加入香港理工大学应用数学系之前，乔博士于2008年8月到2011年12月在香港浸会大学数学系任职助理教授，于2006年7月到2008年7月在美国北卡莱罗纳州立大学科学工程计算研究中心从事博士后研究。
乔博士主要从事数值微分方程方面算法设计及分析，近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文40余篇，文章被合计引用300余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖。
摘要：In this work, we construct exponential time differencing (ETD) schemes for solving the nonlocal Allen-Cahn (NAC) equation. Since the solution to the NAC equation satisfies the maximum principle, numerical approximations preserving the maximum principle in the discrete sense are highly desirable at both physical and mathematical levels. Our numerical schemes are obtained by using the quadrature-based finite difference method for the spatial discretization and applying ETD-based approximations on the temporal integration. We establish the discrete maximum principle by using the properties of matrix exponentials, and then the energy stability and the maximum-norm error estimates are obtained in the discrete sense. In addition, we also prove the asymptotic compatibility of the proposed scheme, which implies the robustness of numerical approximations to the NAC equation. The convergence rates are verified numerically with respect to the discretization and the nonlocal parameters. A further numerical investigation is carried out for the steady state solutions on the relationship between the discontinuities and the nonlocal parameters.
