报告题目：非局部Allen-Cahn方程保持最大值原理的指数时间差分格式

（Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen-Cahn Equation）

报告人：鞠立力   美国南卡罗来纳大学教授、中国海洋大学客座教授

时 间：2018年6月26号（周二）下午15:00

地 点：文理楼254报告厅

报告摘要：The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satisfies the maximum principle as its local counterpart. In this talk, we develop and analyze first and second order exponential time differencing (ETD) schemes for solving the NAC equation, which unconditionally preserve the discrete maximum principle. The fully discrete numerical schemes are obtained by applying the stabilized ETD approximations for time integration with the quadrature-based finite difference discretization in space. We derive their respective optimal maximum-norm error estimates and further show that the proposed schemes are asymptotic compatible, i.e., the approximate solutions always converge to the classic Allen-Cahn solution when the horizon, the spatial mesh size and the time step size go to zero. We also prove that the schemes are energy stable in the discrete sense. Various experiments are performed to verify these theoretical results and to investigate numerically the relationship between the discontinuities and the nonlocal parameters.

报告人简介：

鞠立力，美国南卡罗来纳大学数学系教授、中国海洋大学“绿卡人才工程”客座教授、美国工业与应用数学学会（SIAM）成员。主要从事数值计算方法与分析、网格优化、图像处理、非局部模型、高性能科学计算及其在材料与地球科学中的应用等方面的研究。至今已发表科研论文80余篇，学术google引用近2300余次。先后主持多项由美国国家科学基金会(NSF)和美国能源部(DOE)等联邦机构资助的科研项目，总课题金额超过200万美元。2012至2017年担任数值分析领域国际顶尖学术期刊SIAM Journal on Numerical Analysis编委。与合作者关于合金微结构演化在“神威·太湖之光”超级计算机上的相场模拟工作入围2016年国际高性能计算应用最高奖—“戈登·贝尔”奖提名。

理学院  科技处 国际合作与交流处

2018-06-20