报告人：李精伟（北京师范大学）

时  间：4月27日上午10:30

地  点：厦大海韵园数理大楼天元会议室686

内容摘要:

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 consider the MBP and corresponding numerical schemes for the modified Allen-Cahn equation, which is formed by introducing a nonlocal Lagrange multiplier term to enforce the mass conservation. We first derive sufficient conditions on the nonlinear potentials under which the MBP holds and provide some concrete examples of nonlinear functions. Then we develop first and second order stabilized exponential time differencing schemes for time integration, which are linear schemes and unconditionally preserve the MBP in the time discrete level. Convergence of these schemes is analyzed as well as their energy stability. Various two and three dimensional numerical experiments are also carried out to validate the theoretical results and demonstrate the performance of the proposed schemes.

个人简介：

李精伟博士，2015年毕业于新疆大学数学系获理学学士学位；2019年前往美国南卡罗来纳大学数学系短期访问一年，师从鞠立力教授；2020年在新疆大学获得计算数学博士学位，师从冯新龙教授；2020年至今在北京师范大学数学科学学院从事博士后研究，师从蔡勇勇教授。主要关注数值计算方法与分析、曲面拟合、无网格插值等。在SIAM Journal on Scientific Computing, Journal of Scientific Computing, Computer Physics Communications, Numerical Method for Partial Differential Equation等SCI收录期刊发表文章10余篇。

联系人：熊涛