报告题目：Unconditionally MBP-preserving linear schemes for convective Allen-Cahn equations

主讲人：李精伟 副教授 （兰州大学）

时间：2023年06月12日（周一）15:00 —16:00

地点：理学院317学习室

主办单位：理学院

主讲人简介：

  李精伟，兰州大学副教授，2015年毕业于新疆大学数学系获理学学士学位；2019年到2020年在美国南卡罗来纳大学数学系访问，师从鞠立力教授；2020年毕业于新疆大学获得计算数学博士学位，师从冯新龙教授；2020年到2022年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，并担任助理研究员。2021年获批中国博士后科学基金第70次面上项目。2023年进入兰州大学工作。主要关注数值计算方法与分析、相场方程保结构算法、计算流体力学、无网格插值等。在SIAM Journal on Scientific Computing, Journal of Computational Physics, Journal of Scientific Computing, Computer Physics Communications, Numerical Method for Partial Differential Equation, Communications in Mathematical Sciences等SCI期刊发表文章16篇。

摘要：

  The maximum bound principle (MBP) is an important property for semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initial and boundary conditions and nonlinear operator preserves for all time a uniform pointwise bound in absolute value. It has been a challenging problem to design unconditionally MBP-preserving high-order accurate time-stepping schemes for these equations. Du Qiang et al have estiblished a unified analysical framework on the MBP preserving scheme for the semilinear parabolic equations which in this talk will be extended to convective Allen-Cahn equation. The key in numerical discretizing the convective Allen-Cahn equation is how to efficiently treat the convective term to ensure the MBP holds. We present two different strategies to discretize the convective term, which are linear schemes and unconditionally preserve the MBP in the time discrete level. Convergence of these schemes is analyzed. Various two and three dimensional numerical experiments are also carried out to validate the theoretical results and demonstrate the performance of the proposed schemes. These work are joint with Cai Yongyong, Ju Lili, Lan Rihui, Wang Xiaoqiang et al.