A hierarchical approach for multicontinuum homogenization in high contrast media

主讲人：杨银 湘潭大学教授

时间：2026年4月17日15：00

地点：徐汇校区三号楼332报告厅

举办单位：数理学院

主讲人介绍：杨银，湘潭大学教授，博士生导师。现任湘潭大学数学与计算科学学院院长、湖南国家应用数学中心副主任。主要从事偏微分方程数值解、复杂系统建模、深度学习等领域的研究。

内容介绍：In this talk, we propose a hierarchical multicontinuum homogenization framework. The core idea is to define hierarchical macroscopic points and solve the constrained problems on grids of varying resolutions. The local solutions are decomposed into the linear interpolation of contributions inherited from preceding levels and an additional correction term. This combination is substituted into the original constrained problems, and the correction term is resolved using finite element (FE) grids of varying sizes, depending on the level of the macropoint. By normalizing the computational cost of fully resolving the local problem to O(1), we establish that our approach incurs a cost of O(Lη(1-L)d), highlighting substantial computational savings across hierarchical layers L, coarsening factor η, and spatial dimension d. Numerical experiments validate the effectiveness of the proposed method in media with slowly varying properties, underscoring its potential for efficient multiscale modeling.