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報(bào)告題目：Explicit high-order unconditionally structure-preserving schemes for the conservative Allen-Cahn equations

主講人：張弘副教授（國防科技大學(xué)）      

時(shí)間：2021年5月29日（周六）9:00 a.m.

形式：線上講座      

講座鏈接：https://meeting.tencent.com/s/jgdX3Yf7mSlK

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

     摘要：Comparing with the well-known classical Allen-Cahn equation, the modified Allen-Cahn equation which is equipped with a nonlocal Lagrange multiplier or a local-nonlocal Lagrange multiplier, enforces the mass conservation for modeling phase transitions. In this work, a class of up to third-order explicit structure-preserving schemes is proposed for solving these two modified conservative Allen-Cahn equations. Based on the second-order finite difference space discretization, we investigate the newly developed improved stabilized integrating factor Runge-Kutta (isIFRK) schemes for the stabilizing reformulations of the conservative Allen-Cahn equations. We prove that the original stabilized integrating factor Runge-Kutta schemes fail to preserve the mass conservation law when the stabilizing constant $\kappa > 0$ and the initial mass not equals zero, while the isIFRK schemes not only preserve the maximum-principle unconditionally, but also conserve the mass to machine accuracy without any restriction on the time step size. Convergence and energy stability of the proposed schemes are also presented. Furthermore, a series of numerical experiments validate that each reformulation of the conservative Allen-Cahn equations has it own advantage, and the isIFRK schemes can reach the expected high-order accuracy, conserve the mass and preserve the maximum-principle unconditionally.

     主講人簡(jiǎn)介：    

張弘，2012年畢業(yè)于浙江大學(xué)信息與計(jì)算科學(xué)專業(yè)，2014年獲國防科大計(jì)算數(shù)學(xué)碩士學(xué)位，2018年獲荷蘭烏特勒支大學(xué)博士學(xué)位。2020年12月任國防科技大學(xué)數(shù)學(xué)系副教授，碩士生導(dǎo)師，主要從事微分方程保結(jié)構(gòu)算法、自適應(yīng)移動(dòng)網(wǎng)格方法、梯度流問題的研究。在J. Comput. Phys., Commun. Comput. Phys.等期刊發(fā)表論文20余篇。在國際會(huì)議（ICOSAHOM 2018, BIRS 2018, HYP 2016等）上進(jìn)行了多次學(xué)術(shù)報(bào)告和Poster報(bào)告。主持國家自然科學(xué)基金青年項(xiàng)目1項(xiàng)、湖南省自然科學(xué)基金青年項(xiàng)目1項(xiàng)、國防科技大學(xué)研究項(xiàng)目1項(xiàng)。