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Acceleration of self-consistent field iteration for Kohn–Sham density functional theory
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2024-12-09 , DOI: 10.1016/j.aml.2024.109422
Fengmin Ge, Fusheng Luo, Fei Xu

Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent field iterations, this paper proposes a novel acceleration algorithm, which utilizes some approximate solutions to fit the convergence trend of errors and then obtains a more accurate approximate solution through extrapolation. This novel algorithm differs from previous acceleration schemes in terms of both its ideology and form. Besides using the combination of the derived approximations, we also predict a more accurate solution based on the decreasing trend of error. The significant acceleration effect of the proposed algorithm is demonstrated through numerical examples.

中文翻译:


Kohn-Sham 密度泛函理论的自洽场迭代加速



密度泛函论计算涉及复杂的非线性模型,这些模型需要迭代算法来获得近似解。迭代次数直接影响迭代算法的计算效率。然而,对于复杂的分子系统,经典的自洽场迭代要么不收敛,要么收敛缓慢。为了提高自洽场迭代的效率,该文提出了一种新的加速算法,该算法利用一些近似解来拟合误差的收敛趋势,然后通过外推获得更准确的近似解。这种新颖的算法在意识形态和形式上都与以前的加速方案不同。除了使用推导的近似值的组合外,我们还根据误差的递减趋势预测更准确的解。通过数值算例证明了所提算法的显著加速效应。
更新日期:2024-12-09
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