报告题目：Generalized multiscale finite element method for highly heterogeneous compressible flow
报告人：付书彬博士（维斯康大学麦迪逊分校）
邀请人：李秋齐
时间：2022 年 6 月 2 日 (星期四) 9:00-10:00 AM
报告形式：在线报告 ( 腾讯会议）
腾讯会议号：664 939 808
入会链接：https://meeting.tencent.com/dm/2vLbt5BmfqJA
报告摘要
In this talk, I will introduce the generalized multiscale finite element method (GMsFEM) for single phase
compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to
construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is
efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous
convergence analysis is performed for two types of snapshot spaces. The analysis indicates that the con-
vergence rates of the proposed multiscale method depend on the coarse meshsize and the eigenvalue decay
of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online
multiscale basis is added to the offline space. The construction of online multiscale basis is based on a care-
fully design error indicator motivated by the analysis. We find that online basis is particularly important
for the singular source. Rich numerical tests on typical 3D highly heterogeneous medias are presented to
demonstrate the impressive computational advantages of the proposed multiscale method.
专家简介
付书彬博士现为维斯康大学麦迪逊分校数学系博士后，他先后毕业于四川大学和德州农工大。付博
士的主要研究兴趣是多尺度有限元方法特别是其在地球物理, 大气海洋学，石油工程和水文学等领域
的应用。他已在 Multiscale Model simulation, Computer Methods in Applied Mechanics and Engineering,
Journal of Computational Physics, Geophysical Journal International 和 Water Resources Research 等期刊
发表多篇论文。
