论文标题
金属系统密度功能理论模型的数学分析和数值近似
Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems
论文作者
论文摘要
在本文中，我们研究了金属系统的集合Kohn-Sham密度功能理论的能量最小化模型，其中涉及伪元素值矩阵和一般涂抹方法。我们研究能量功能的最小化器的不变性和存在。我们提出了一种自适应双步尺寸策略和相应的预处理共轭梯度方法，用于解决能量最小化模型。在一些温和但合理的假设下，我们证明了算法的全球融合。数值实验表明，我们的算法有效，尤其是对于大型金属系统。特别是，我们的算法为某些金属系统产生收敛的数值近似值，传统的自洽场迭代无法收敛。
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance and the existence of the minimizer of the energy functional. We propose an adaptive double step size strategy and the corresponding preconditioned conjugate gradient methods for solving the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence of our algorithms. Numerical experiments show that our algorithms are efficient, especially for large scale metallic systems. In particular, our algorithms produce convergent numerical approximations for some metallic systems, for which the traditional self-consistent field iterations fail to converge.
