1. MATHEMATICAL ANALYSIS AND NUMERICAL APPROXIMATIONS OF DENSITY FUNCTIONAL THEORY MODELS FOR METALLIC SYSTEMS.
- Author
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XIAOYING DAI, DE GIRONCOLI, STEFANO, BIN YANG, and AIHUI ZHOU
- Subjects
MATHEMATICAL analysis ,DENSITY functional theory ,NUMERICAL analysis ,LARGE scale systems ,MODEL theory ,CONJUGATE gradient methods - Abstract
In this paper, we investigate the energy minimization model arising in 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 of the energy functional and the existence of the minimizer of the ensemble Kohn--Sham model. We propose an adaptive twoparameter step size strategy and the corresponding preconditioned conjugate gradient methods to solve the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence for the gradients of the energy functional produced by 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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