报告题目：Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals

报 告 人：乔中华 教授（香港理工大学）

报告时间：2024年10月11日（周五）上午10：00

报告地点：数学楼115（大报告厅）

校内联系人：李崇君 教授  联系方式：84708351-8310

报告摘要：In this talk, we propose two efficient fully discrete schemes for Q-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) Q-tensor flows, the unconditional maximum-bound-principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes.

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，中科院数学与系统科学研究院——香港理工大学应用数学联合实验室港方副主任，中国工业与应用数学学会理事，中国数学会计算数学分会副理事长。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80余篇，文章被合计引用3000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奖。