报告时间： 2021 年 12 月 15 日 16:00–17:30
报告地点：腾讯会议
会 议 号： 901733120
邀请人：宋怀玲
摘要：
The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the wellknown AllenCahn equation. While some commonlyused firstorder 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 higherorder schemes in order to have such simultaneous preservation. In this paper, we develop and analyze novel first and secondorder linear numerical schemes for a class of AllenCahn 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. Some experiments are also carried out to numerically illustrate the properties
and performance of the proposed schemes.
报告人简介：
乔中华，香港理工大学教授。2006 年在香港浸会大学获得博士学位。主要从事数值微分方程方面算法设计及分析，特别是相场方程的数值模拟及计算流体力学的高效算法。至今在 SIAM Rev、SIAM J.Numer.Anal、SIAM J. Sci Comp、Numer Math、Math Comp、J. Comp Phys 等计算数学 顶级期刊上发表学术论文 60 余篇，文章被合计引用 1200 余次。2013 年 获香港研究资助局颁发的杰出青年学者奖，2018 年获得香港数学会青年学者奖，2020 年获得香港研究资助局研究学者奖。
poster_乔中华.pdf
