汇报标题 (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尺度模型降阶)
汇报人 (Speaker)：杨银 教授（湘潭大学）
汇报功夫 (Time)：2024年12月10日(周二) 15:30-17:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：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.
