报告地点：行健楼学术活动室526
摘要：Finite element methods for H(curl) interface equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential obstacle for almost all the interface-unfitted mesh methods in the literature regarding the application to H(curl) interface problems. In this talk, we will present a novel immersed virtual element method (IVEM) for solving a 3D H(curl) interface problems. The motivation is to combine the conformity of virtual element spaces and robust approximation capabilities of immersed finite element spaces. The proposed method is able to achieve optimal convergence for a class of 3D H(curl) interface problem. To develop a systematic framework, a de Rham complex for H1, H(curl), and H(div) interface problems will be established based on which the Hiptmair-Xu (HX) preconditioner can be adapted to develop a fast solver for the H(curl) interface problem. An efficient polyhedral mesh generator is also provided to generate a polyhedral mesh with an interface fitted boundary triangulation.
This is a joint work with Shuhao Cao and Ruchi Guo.
报告人简介：陈龙教授任职于加州大学欧文分校（UCI）数学系。 1997年毕业于南京大学，2000年获北京大学硕士学位，2005年获宾夕法尼亚州立大学博士学位，博士生导师为许进超教授。 2005年至2007年在加州大学圣地亚哥分校和马里兰大学帕克分校从事博士后研究。 2007年起在UCI工作，2011年获得终身教职，2015年晋升为正教授。
陈教授的研究领域是偏微分方程的数值解，尤其是有限元方法的设计与分析。陈教授开发了iFEM有限元软件包，为有限元方法的教学和研究提供了极大的便利。陈教授在国际知名期刊发表学术论文80余篇，担任多个SCI期刊编委。从他开始工作到现在，陈教授一直得到美国国家科学基金会的持续支持。另外，他还创立了微信公众号《CAM 传习录》(CAMtips)，分享关于计算和应用数学的学习和研究方法。
更多详情请访问陈教授主页：//www.math.uci.edu/~chenlong/
