多尺度建模中的自适应数值方法及其应用Adaptive Numerical Methods for Multiscale Modeling and Applications

讲座时间 Datetime: 

星期一, 2019/07/01 - 从 14:30 到 16:00

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

潘世猛 博士

单位 Affiliation: 

香港中文大学

报告摘要 Abstract: 

In this talk, we present the adaptive numerical methods within the framework of generalized multiscale finite element method (GMsFEM). There are four parts in this work. In this first part, we study both the offline and online goal-oriented adaptivity to drive error reduction in some specific quantities of interest instead of usual energy norm in finite element community.

In the second part, we apply the online residual-driven GMsFEM to solve the dynamic bi-orthogonal system arising from the research of uncertainty quantification. This problem involves multiscale and random features, which make the mathematical model more complicated.

In the third part, we will develop the online adaptive algorithm for the constraint energy minimizing GMsFEM. This methodology is a variant of the generalized multiscale finite element method and requires to resolve the basis function in an appropriate chosen oversampling regions with least local energy norm.

Finally, we explore the application of CEM-GMsFEM to solve the mixed wave equation. We prove that the proposed algorithm is of first-order convergence with respect to the coarse mesh size.