报告题目: Generalized SAV exponential integrator schemes for Allen–Cahn type gradient flows

报告人：乔中华教授 香港理工大学

摘要：The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the well-known Allen–Cahn equation. While some commonly-used first-order time stepping schemes have turned out to preserve unconditionally both energy dissipation law and MBP for the equation, restrictions on the time step size are still needed for existing secondorder or even higher-order schemes in order to have such simultaneous preservation. In this paper, we develop and analyze novel first- and second-order linear numerical schemes for a class of Allen–Cahn type gradient flows. Our schemes combine the generalized scalar auxiliary variable (SAV) approach and the exponential time integrator with a stabilization term, while the standard central difference stencil is used for discretization of the spatial differential operator. We not only prove their unconditional preservation of the energy dissipation law and the MBP in the discrete setting, but also derive their optimal temporal error estimates under fixed spatial mesh. Numerical experiments are also carried out to demonstrate the properties and performance of the proposed schemes.

报告时间：2022年5月4日 15:00-16:00

地点：腾讯会议ID：703-481-606

报告邀请人：科学与工程计算科研团队

报告人简介：乔中华博士于2006年在香港浸会大学获得博士学位，现为香港理工大学应用数学系教授。乔博士主要从事数值微分方程方面算法设计及分析，近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文60余篇，文章被合计引用1300余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖，于2018年获得香港数学会青年学者奖，并且于2020年获得香港研究资助局研究学者称号。