报告题目：Unconditional MBP preservation and energy stability of the stabilized exponential time differencing schemes for the vector-valued Allen-Cahn equations
报 告 人：李精伟
报告时间：1月3日10:20
报告地点： 莲花街校区惟德楼315会议室
报告人照片：
报告人简介：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；2020年毕业于新疆大学获得计算数学博士学位；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，并担任助理研究员。2021年荣获中国博士后科学基金第70次面上项目。2023年至今在兰州大学工作。2023年荣获中国自然科学青年基金项目。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期刊发表文章十余篇。
报告内容简介：The vector-valued Allen-Cahn equations have been extensively applied to simulate the multiphase flow models. In this work, we consider the maximum bound principle (MBP) and corresponding numerical schemes for the vector-valued Allen-Cahn equations. We firstly formulate the stabilized equations via utilizing the linear stabilization technique, and then focus on the bounding constant of the nonlinear function based on the fact that the extremes of a constrained problem will occur in the bounded and convex domain. Later the first- and second-order stabilized exponential time differencing schemes are adopted for temporal integration, which are linear and unconditionally preserve the discrete MBP in the time discrete sense. Moreover, the proposed schemes can be proven to dissipate the original energy instead of the modified energy. Their convergence analysis is also presented. Various numerical examples are performed to verify these theoretical results and demonstrate the efficiency of the proposed schemes.
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数学与统计学院
2025年1月2日
