7月15日 Guanghui Hu教授学术报告

发布时间:2014-07-14

题 目： Real-Time Adaptive Finite Element Solution of Time-Dependent Kohn-Sham Equation
报告人：Assistant Prof. Guanghui Hu
(Department of Mathematics, University of Macau)
时 间：7月15日（周二） 上午10:00-11:00
地 点：旧数学楼104室

Abstract:
In our previous paper [G. Bao, G. H. Hu, and D. Liu, /emph{An $h$-adaptive finite element solver for the calculations of the electronic structures}, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena. in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

个人简历:
Guanghui Hu is an Assistant Professor of the Dept. of Mathematics at University of Macau. He received his BS and MS in Math from Siquan University in 2003 and 2006, respectively, and he received his Ph.D. in Dept. of Mathematics from Hongkong Baptist University in 2009. He is a visiting Research Associate of the Dept. of Mathematics at Michigan State University from 2010 to 2012. His current research interests include electronic structure calculations, computational fluid dynamics, and adaptive methods of partial differential equations.

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