6月21日 陈龙教授学术报告

发布时间:2024-06-20

报告题目：Finite Element Complexes

主讲人：Long Chen. University of California at Irvine 

报告时间：2024年6月21日，9:00-11:00

报告地点：bat365在线中国登录入口A501

主持人：邹青松教授

摘要：

A Hilbert complex consists of a sequence of Hilbert spaces interconnected by a series of closed, densely defined linear operators, such that the composition of two consecutive maps equals zero. The de Rham complex serves as the most prominent example. Finite element complexes arise from discretizing Hilbert complexes by substituting infinite dimensional Hilbert spaces with finite dimensional subspaces, based on a triangulation of the underline domain. 

This presentation provides an overview of finite element complex construction, showcasing the finite element de Rham complex through a geometric decomposition method. The construction is extended to additional finite element complexes, such as the Hessian complex, elasticity complex, and divdiv complex, using the Bernstein-Gelfand-Gelfand (BGG) framework.

The resulting finite element complexes hold potential applications in numerical simulations for the biharmonic equation, linear elasticity, general relativity, and other geometry-related PDEs. 

This work is a collaborative effort with Xuehai Huang from Shanghai University of Finance and Economics.

主讲人简介：

Long Chen is currently a Professor of Mathematics at University of California at Irvine (UCI). He graduated from Nanjing University in 1997, obtained a master's degree from Peking University in 2000, and finished Ph.D from Pennsylvania State University in 2005. His doctoral supervisor is Professor Jinchao Xu. From 2005 to 2007, he worked as a postdoctoral fellow at the University of California, San Diego and the University of Maryland, College Park. Since 2007, he has been working at UCI, and was tenured in 2011, and promoted to full professor in 2015.

Professor Chen's research field is the numerical solution of partial differential equations, especially the design and analysis of finite element methods. Professor Chen developed the iFEM finite element software package, which provided great convenience for the teaching and research of finite element methods. Professor Chen has published more than 80 academic papers in internationally renowned journals, and serves on the editorial board of several SCI journals. Since his work till now, Professor Chen has been constantly supported by the National Science Foundation. In addition, he has also created a WeChat account  CAMtips, where he shares learning and research methods related to computational and applied mathematics.

For more detail, please visit Professor Chen's homepage: https://www.math.uci.edu/~chenlong/.