报告题目：Immersed Finite Element Methods for Interface Problems Basic idea,Development,Analysis,and Applications
报告人：Xu Zhang 教授（Mississippi State University)
报告时间：2017年6月8日（周四）上午10:00-11:00
报告地点：数学与统计学院金融实验室

Abstract:

Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the convergence could be impaired. Immersed finite element (IFE) methods allow the interface to be embedded in elements, so that Cartesian meshes can be used for problems with non-trivial interface geometry.

In this talk, we start with an introduction about the basic ideas of IFE methods for the second-order elliptic equation. We will present challenges of conventional IFE methods, and introduce some recent advances in designing more accurate and robust IFE schemes. Mathematical convergence theories and some numerical experiments will be presented. Finally, we will demonstrate how IFE methods can be applied to more complicated interface model problems.

Biography:

Dr. Xu Zhang is currently an assistant professor of mathematics at Mississippi State University. Dr. Zhang received his Bachelor (2005) and Master degrees (2008) in computational mathematics from Sichuan University. He received the Ph.D. in mathematics from Virginia Tech in 2013. Before joining MSU, Dr. Zhang worked at Purdue University during 2013-2016 as a Golomb visiting assistant professor.

Dr. Zhang’s research interests are in scientific computing and numerical analysis. He specializes in numerical methods for partial differential equations. Recently his research focuses on immersed finite element methods for interface problems: algorithm development, implementation, error analysis, and applications.

欢迎各位师生参加。