报告题目：Explicit high-order unconditionally structure-preserving schemes for the conservative Allen-Cahn equations

主讲人：张弘副教授（国防科技大学）      

时间：2021年5月29日（周六）9:00 a.m.

形式：线上讲座      

讲座链接：https://meeting.tencent.com/s/jgdX3Yf7mSlK

主办单位：统计与数学学院

     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.

     主讲人简介：    

张弘，2012年毕业于浙江大学信息与计算科学专业，2014年获国防科大计算数学硕士学位，2018年获荷兰乌特勒支大学博士学位。2020年12月任国防科技大学数学系副教授，硕士生导师，主要从事微分方程保结构算法、自适应移动网格方法、梯度流问题的研究。在J. Comput. Phys., Commun. Comput. Phys.等期刊发表论文20余篇。在国际会议（ICOSAHOM 2018, BIRS 2018, HYP 2016等）上进行了多次学术报告和Poster报告。主持国家自然科学基金青年项目1项、湖南省自然科学基金青年项目1项、国防科技大学研究项目1项。