报告问题 (Title)：Multiscale Model Reduction in Heterogeneous Perforated Domains Based on CEM-GMSFEM （基于CEM-GMSFEM的非均质有孔区域多标准模子降阶)

报告人 (Speaker)：杨银 教授（湘潭大学）

报告时间 (Time)：2024年12月10日(周二) 15:30-17:00

报告所在 (Place)：校本部GJ303

约请人(Inviter)：李常品、蔡敏

主理部分：理学院数学系

报告摘要：In this report, we introduce a new numerical approach framework based on the Constrained Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for simulating heterogeneous porous materials. Due to the scale differences between pores and between the pores and the computational domain, traditional methods often incur prohibitive computational costs. To address this issue, we employ the CEM-GMsFEM method, which captures fine-scale microscopic information through local multiscale basis functions. Our method consists of two stages: the offline stage and the online stage. In the offline stage, we first solve the eigenvalue problem in coarse elements and then solve the minimization problem in oversampling regions to construct local multiscale basis functions. In the online stage, we can incorporate global information, such as source terms. Numerical examples demonstrate the effectiveness of this method in solving Poisson's equation and linear elasticity problems in heterogeneous porous materials.