Title: Fast Numerical Methods for Electronic Structure Calculations 

Speaker: Chao Yang 

時間：2014年11月20日（周四）下午4:00 

地點：五號樓 5層 A507會議室 

Abstract: 

The Kohn-Sham density functional theory (KSDFT) is the most widely used theory for studying electronic properties of molecules and solids. It reduces the need to solve a many-body Schrodinger's equation to the task of solving a system of single-particle equations coupled through the electron density. These equations can be viewed as a nonlinear eigenvalue problem. Although they contain far fewer degrees of freedom, these equations are more difficult in terms of their mathematical structures.  In this talk, I will give an overview on efficient algorithms for solving this type of problems.  A key concept that is important for understanding these algorithms is a nonlinear map known as the Kohn Sham map. The ground state electron density is a fixed point of this map. I will describe properties of this map and its Jacobian.  These properties can be used to develop effective strategies for accelerating Broyden's method for finding the optimal solution. They can also be used to reduce the computational complexity associated with the evaluation of the Kohn Sham map, which is the most expensive step in a Broyden iteration. 

Biography: 

Chao Yang (楊超) is a staff scientist at the Computational Research Division of the Lawrence Berkeley National Laboratory in USA. He received his B.S. in Computer Science and Mathematics from Central Missouri State University in 1992, his M.A. in Mathematics from the University of Kansas in 1994, and his Ph.D in Computational Science and Engineering from the Rice University in 1998. Chao is a developer of the famous eigenvalue calculation software ARPACK and the main developer of several other important software packages. He received the Spot Award for his contribution to the DOE's SciDAC projects.