报告题目：A hierarchical approach for multicontinuum homogenization in high contrast media

报告人：杨银 教授

报告时间：2026年5月28日 (星期四)上午 09:00-10:30

报告地点：文科综合楼E-2029会议室

欢迎广大师生参加！

科研处  学科建设办公室  数理学院（应用数学研究所）

2026年5月25日

报告人简介：

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。

报告摘要：

A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct physical properties and solves a series of constrained cell problems to capture localized information for each continuum. However, solving all these cell problems on very fine grids at every macroscopic point is computationally expensive, which is a common limitation of most homogenization approaches for non-periodic problems. To address this challenge, 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.