【理学院】理学论坛第184次学术活动

发布时间:2021-11-11   浏览次数:1647   发布部门:科学技术处

报告题目1Adaptive FEM for Helmholtz equation with large wave number

报告人:武海军教授

报告人单位:南京大学

时间2021111215:00-16:00

地点:仙林校区教2-314

主办单位:理学院

 

报告内容A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates the true error of the FE solution for the mesh size hin the preasymptotic regime, which is first observed by Babus ̌ka, et al. for an one dimensional problem. By establishing an equivalence relationship between the error estimators for the FE solution and the corresponding elliptic projection of the exact solution, an adaptive algorithm is proposed and its convergence and quasi-optimality are proved under condition thatk^3 h_0^(1+α) is sufficiently small, whereh_0 is the initial mesh size and 1/2<α≤1is a regularity constant depending on the maximum reentrant angle of the domain. Numerical tests are given to verify the theoretical findings and to show that the adaptive continuous interior penalty finite element method (CIP-FEM) with appropriately selected penalty parameters can greatly reduce the pollution error and hence the residual type error estimator for this CIP-FEM is reliable and efficient even in the preasymptotic regime.

 

报告人简介:武海军,南京大学数学系教授,博导。2003年至今任教于南京大学数学系,2005年被评为副教授,2006年被评为教授。曾于2003-2004年于美国密歇根州立大学任访问学者,20061月至5月于美国韦恩州立大学任访问学者。武海军教授于2006年获得教育部新世纪优秀人才支持计划支持,2012年获得江苏省数学杰出成就奖,2015年获得国家杰出青年科学基金资助,在SIAM J. Numer. Anal.Math. Comput.SIAM MMS等杂志上发表论文40余篇。武海军教授的主要研究领域为自适应有限元法、高波数散射问题及界面问题的数值解法。

 


 

报告题目2Combined MsFEMs for the multiscale elliptic problems with well-singularities

报告人:邓卫兵教授

报告人单位:南京大学

时间2021111216:00-17:00

地点:仙林校区教2-314

主办单位:理学院

 

报告内容In this talk, we discuss how to solve the multiscale problems which may have well-singularities in some special portions of the computational domain. For example, in the simulation of steady flow transporting through highly heterogeneous porous media driven by extraction wells, the singularities lie in the near-well regions. We first review some existed methods, and then introduce a new combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique.  The basic idea of the combined method is to utilize the traditional finite element method (FEM) directly on a fine mesh of the problematic part of the domain and using the LOD--based MsFEM on a coarse mesh of the other part. The key point is how to define local correctors for the basis functions of the elements near the coarse and fine mesh interface, which require meticulous treatment. The error analysis is carried out for highly varying coefficients, without any assumptions on scale separation or periodicity. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

 

报告人简介:邓卫兵,南京大学数学系教授,博导。1995年至今任教于南京大学数学系,2003年被评为副教授,2008年被评为教授。2003-2004年于中科院计算数学所从事博士后工作,2007-2008年于加州理工大学应用与计算数学系访问。现为南京大学数学系副主任,江苏省实验教学与实践教育中心数学技术与能力综合训练中心主任。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。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,在J. Comput. Phys.SIAM MMSAppl. Numer. Math.等杂志发表论文30余篇。邓卫兵教授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。