广州数学大讲坛第一期
第七讲——香港大学王亚婷助理教授学术报告
题目： Multirate partially explicit scheme for multiscale flow problems
时间：2022年03月31日（周四）下午13：30－15：30
地点：腾讯会议（会议ID：100725471）
报告人：王亚婷
入会链接：https://meeting.tencent.com/dm/CiIT4TLVocg9
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.
报告人简介：
王亚婷，香港大学数学系助理教授，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。主要从事多尺度模型降阶和相关的深度学习问题。
