報告題目：Unconditional MBP preservation and energy stability of the stabilized exponential time differencing schemes for the vector-valued Allen-Cahn equations

報 告 人：李精偉

報告時間：1月3日10:20

報告地點： 蓮花街校區惟德樓315會議室

報告人照片：

報告人簡介：李精偉，蘭州大學副教授，2015年畢業于新疆大學數學系獲理學學士學位；2019年到2020年在美國南卡羅來納大學數學系訪問；2020年畢業于新疆大學獲得計算數學博士學位；2020年到2022年在北京師范大學數學科學學院從事博士后研究，并擔任助理研究員。2021年榮獲中國博士后科學基金第70次面上項目。2023年至今在蘭州大學工作。2023年榮獲中國自然科學青年基金項目。主要關注數值計算方法與分析、相場方程保結構算法、計算流體力學、無網格插值等。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期刊發表文章十余篇。

報告內容簡介：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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數學與統計學院
2025年1月2日