报告题目：Energy-Dissipative Spectral Renormalization Exponential Integrator Method for Gradient Flow Problems
报 告 人：乔中华教授 香港理工大学
报告摘要：In this talk, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and achieve high-order accuracy in time. To accomplish this, our method first incorporates the energy dissipation law into the target gradient flow equation by introducing a time-dependent spectral renormalization (TDSR) factor. Then, the coupled equations are discretized using the spectral approximation in space and the exponential time differencing (ETD) in time. Finally, the resulting fully discrete nonlinear system is decoupled and solved using the Picard iteration at each time step. Furthermore, we introduce an extra enforcing term into the system for updating the TDSR factor, which greatly improves the solvability and the time step size restriction of the proposed method and enhances its computational efficiency. Extensive numerical tests with various gradient flows are presented to demonstrate the accuracy and effectiveness of our method as well as its high efficiency when combined with an adaptive time-stepping strategy for long-term simulations.
报告人简介：乔中华，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，香港数学会常务理事，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。 乔教授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70余篇，文章被合计引用2200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。
报告时间：2024年8月24日 15:30-17:00
报告地点：文渊楼 B536
主办单位：数学与统计学院
