Wang Jian, Wang Yu, Yu Shaoying, Kolb Dietmar
School of Science, Huzhou University, Zhejiang 313000, People's Republic of China.
J Phys Condens Matter. 2005 Jun 29;17(25):3701-15. doi: 10.1088/0953-8984/17/25/001. Epub 2005 Jun 10.
We apply a nonlinear multigrid algorithm, named the full approximation storage (FAS) scheme, to the Kohn-Sham equations for pseudopotential band structure calculations. Traditionally, the nonlinear self-consistent problem is linearized into successive fixed potential eigenvalue problems with potentials updated between them. In the new method, the self-consistent problem is solved directly with the FAS scheme. First, the error of self-consistence in density is calculated; then, an FAS coarse grid problem is defined and solved; finally, a correction is interpolated to the fine grid to modify the density. The eigenvalue problem is integrated inside the FAS scheme, and evolves along with the self-consistent problem within the FAS frame. Calculations are demonstrated for Si and Al.
我们将一种名为全近似存储（FAS）格式的非线性多重网格算法应用于赝势能带结构计算的科恩-沈方程。传统上，非线性自洽问题被线性化为连续的固定势本征值问题，且在这些问题之间更新势。在新方法中，自洽问题通过FAS格式直接求解。首先，计算密度中的自洽误差；然后，定义并求解一个FAS粗网格问题；最后，将校正值插值到细网格以修正密度。本征值问题在FAS格式内进行积分，并在FAS框架内与自洽问题一起演化。文中给出了硅和铝的计算结果。
