报告时间：2022/10/11 13:30-15:00
重复周期：2022/09/13-2022/12/27 10:00-16:00, 每周 (周二)
报告人：邓卫兵 教授
腾讯会议：932-7827-6364
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报告人简介：邓卫兵，南京大学数学系教授，博导。1988年本科毕业于南京大学，1995年获南京大学计算数学硕士学位，2002年获南京大学应用数学博士学位，2003年至2004年于中科院计算数学所从事博士后工作，2007年至2008年于加州理工大学应用与计算数学系访问。现阶段主要研究多尺度问题的分析和计算，数值均匀化方法，以及基于数据和机理综合驱动的建模方法。研究成果主要发表在《Journal of Computational Physics》、《Multiscale Modeling & Simulation》、《Numerical Methods for Partial Differential Equations》、《Applied Numerical Mathematics》、《Nonlinear Analysis》等杂志上。目前主持科技部重点研发计划课题和国家自然科学基金项目各一项，参与国家自然科学基金重大项目一项。曾主持和参与多项国家自然科学基金项目、江苏省自然科学基金创新人才项目等。
报告摘要：
In this talk, a new combined multiscale finite element method is proposed to solve the multiscale elliptic problems with rough boundaries. To design a numerical method for this kind of problems is difficult because that the microscopically geometrical information of the boundary and oscillation information of the coefficient should be taken into account simultaneously, which usually requires a very fine mesh. The main idea of the proposed method is to adopt unfitted fine scale meshes on the rough boundary by using the cut finite element, and adopt the coarse scale meshes for the other part by using the recently developed local orthogonal decomposition (LOD) technique. Through this way, the introduced method can deal with arbitrarily rough boundaries and cut down some unnecessary computational effort. To ensure that the discrete systems are well-posed, we utilize the penalty technique on the artificial interface between coarse and fine meshes as well as on the Dirichlet boundary. The ghost penalty technique is used on the Dirichlet boundary to avoid the ill-condition of the system matrix. The error estimate and the condition number of the system matrix for the proposed method are derived without any periodic assumptions on the coefficient and boundary shape. Especially, the result is independent of the way that the boundary cut the mesh. Numerical experiments further confirm the theoretical results and demonstrate the accuracy and efficiency of the proposed method.
邀请人：杜锐