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：Multirate partially explicit scheme for multiscale flow problems

报告人：王亚婷 副教授 西安交通大学best365亚洲版登录

邀请人：董灏博士

报告时间：2022年9月23日下午2:30

报告地点：腾讯会议ID：974-935-263 会议链接：https://meeting.tencent.com/dm/zSY1Hfi8MuBi

报告人简介：王亚婷，西安交通大学best365亚洲版登录副教授，博导，入选西安交通大学青年拔尖人才计划(B类)。2018年获Texas A&M University博士学位，2018-2021年，赴普渡大学开展博士后研究，2021-2022年为香港大学数学系助理教授，2022年7月起任职于西安交通大学best365亚洲版登录。主要从事多尺度模型降阶和相关的深度学习方法研究，已在计算数学领域顶级期刊SIAM Journal on Scientific Computing、Journal of Computational Physics、Multiscale Modeling & Simulation等发表论文多篇。

报告摘要：For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a stable temporal splitting scheme where the time step size is independent of the contrast. Consider the parabolic equation with heterogeneous diffusion parameter, the flow rates vary significantly in different regions due to the high-contrast features of the diffusivity. In this talk, we aim to introduce a multirate partially explicit splitting scheme to achieve efficient simulation with the desired accuracy. We first design multiscale subspaces to handle flow with different speeds. Then a multirate time stepping is introduced for the partially explicit scheme. The stability of the multirate methods is analyzed for the partially explicit scheme. Moreover, we derive local error estimators corresponding to the two components of the solutions and provide an upper bound of the errors. An adaptive local temporal refinement framework is then proposed to achieve higher computational efficiency.

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