金属体系密度泛函理论模型的数学分析和数值逼近
Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems
摘要：
本文研究了金属体系的系综Kohn-Sham密度泛函理论的能量极小化模型，其中包含一个赝本征值矩阵和一个一般的涂抹方法.研究了能量泛函的不变性和极小元的存在性。提出了求解能量极小化模型的自适应双步长策略和相应的预条件共轭梯度法。在一些温和但合理的假设下，我们证明了我们的算法的整体收敛。数值实验表明，我们的算法是有效的，特别是对大规模的金属系统。特别是，我们的算法产生收敛的数值逼近的一些金属系统，传统的自洽场迭代无法收敛。
英文摘要：
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.
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