报告题目：Unconditionally MBP-preserving exponential time differencing schemes for conservative Allen-Cahn equations

报告时间：2021年12月27日（星期一）上午9:30-12:30

报告平台：腾讯会议，ID: 138175000

报告人：鞠立力教授（美国南卡莱罗纳大学）

摘要：In comparison with the Cahn-Hilliard equation, the classic Allen-Cahn equation satisfies the maximum bound principle (MBP) but fails to conserve the mass along the time. In this work, we study MBPs and corresponding MBP-preserving numerical schemes for two types of modified Allen-Cahn equations which can conserve the mass exactly. One is formed by introducing a nonlocal Lagrange multiplier to enforce the mass conservation, and the other is achieved through a Lagrange multiplier with both nonlocal and local effects. We propose first and second order stabilized exponential time differencing schemes (ETD) for solving these conservative Allen-Chan equations, which are linear and shown to be unconditionally MBP-preserving in the time discrete sense. Convergence of the two ETD schemes is then analyzed as well as their energy stability. Various numerical experiments in two and three dimensions are also carried out to validate the theoretical results and demonstrate the performance of the proposed schemes.

报告人简介：鞠立力，美国南卡罗来纳大学数学系教授、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100余篇，学术google引用近4000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。