Fast Numerical Methods for Electronic Structure Calculations
主 题: Fast Numerical Methods for Electronic Structure Calculations
报告人: Chao Yang (Lawerence Berkeley National Laboratory )
时 间: 2014-11-21 14:00 - 15:00
地 点: Room 09 at Quan Zhai, BICMR（主持人：文再文）
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.