活动主题：计算数学及其交叉学科前沿系列讲座报告
报告题目：Adaptive Space-Time Methods for Multiscale Flow Problems Using a Partially Explicit Splitting Scheme
报告人：Wing Tat Leung 助理教授 香港城市大学
邀请人：董灏博士
报告时间：2025年6月4日(星期三)下午15:30-19:30
报告地点：南校区会议中心120会议室
报告人简介：Dr. Wing Tat Leung received his bachelor’s degree in mathematics from Chinese University of Hong Kong, in 2010. He received master’s degree in mathematics from Chinese University of Hong Kong, in 2012. He received his PhD in mathematics from Texas A&M Univeristy, USA, in 2017. Before joining City University of Hong Kong in 2022, he worked as a visiting assistant professor at UC Irvine. Dr. Wing Tat Leung’s research interests are scientific computation. Research topics include numerical analysis, multiscale method and model reduction.
报告摘要：In this talk, I will present a space-time adaptive framework for efficiently simulating flow problems in multiscale media with high-contrast coefficients. These problems pose significant challenges due to the need to capture non-local effects across scales and the restrictive time step sizes required by explicit schemes in the presence of large coefficient variations. To address these issues, we propose a partially explicit temporal splitting scheme combined with an adaptive multiscale method. Our approach constructs two multiscale subspaces to separately handle fast and slow flow components, using implicit discretization for one and explicit for the other. A multirate time-stepping strategy is employed to accommodate the disparate flow rates across regions. To ensure both accuracy and efficiency, we derive a posteriori error estimators in space and time that guide local enrichment of the multiscale spaces and adaptive refinement of time steps. Starting with a minimal number of basis functions and coarse temporal resolution, the algorithm adaptively improves the solution by introducing energy-minimizing basis functions where needed. I will discuss the stability and convergence analysis of the method, and present numerical results that illustrate its effectiveness in capturing multiscale features while significantly reducing computational cost.
主办单位：学院
