報(bào)告題目：Unconditional MBP preservation and energy stability of the stabilized exponential time differencing schemes for the vector-valued Allen-Cahn equations
報(bào) 告 人：李精偉
報(bào)告時(shí)間：1月3日10:20
報(bào)告地點(diǎn)： 蓮花街校區(qū)惟德樓315會(huì)議室
報(bào)告人照片：
報(bào)告人簡(jiǎn)介：李精偉，蘭州大學(xué)副教授，2015年畢業(yè)于新疆大學(xué)數(shù)學(xué)系獲理學(xué)學(xué)士學(xué)位；2019年到2020年在美國(guó)南卡羅來(lái)納大學(xué)數(shù)學(xué)系訪(fǎng)問(wèn)；2020年畢業(yè)于新疆大學(xué)獲得計(jì)算數(shù)學(xué)博士學(xué)位；2020年到2022年在北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院從事博士后研究，并擔(dān)任助理研究員。2021年榮獲中國(guó)博士后科學(xué)基金第70次面上項(xiàng)目。2023年至今在蘭州大學(xué)工作。2023年榮獲中國(guó)自然科學(xué)青年基金項(xiàng)目。主要關(guān)注數(shù)值計(jì)算方法與分析、相場(chǎng)方程保結(jié)構(gòu)算法、計(jì)算流體力學(xué)、無(wú)網(wǎng)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(fā)表文章十余篇。
報(bào)告內(nèi)容簡(jiǎn)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(shù)學(xué)與統(tǒng)計(jì)學(xué)院
2025年1月2日
