An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory

Gao, Bin; Hu, Guanghui; Kuang, Yang; Liu, Xin

doi:10.1137/20m1355884

Cited by 6 publications

(3 citation statements)

References 47 publications

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“…However, it should be noted that [28] requires an explicit operation in order to preserve the orthogonality of the wave functions and this diminishes the efficiency of the simulations. To overcome this bottleneck, an infeasible method was proposed for minimizing the total energy of a Kohn-Sham system [13], so that the ground state can be gradually obtained, without explicit treatment of the orthogonality.…”

Section: Introductionmentioning

confidence: 99%

A Linearized Structure-Preserving Numerical Scheme for a Gradient Flow Model of the Kohn-Sham Density Functional Theory

Hu¹,

Zhou²

2023

EAJAM

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Dai et al. [Multiscale Model. Simul. 18 (2020)] proposed a gradient flow model and a numerical scheme for ground state calculations in Kohn-Sham density functional theory. It is a feature that orthonormality of all wave functions can be preserved automatically during the simulation which makes such a method attractive towards simulations for large scale systems. In this paper, two extensions are proposed for further improving the efficiency of the method. The first one is a linearization of the original nonlinear scheme. It is shown analytically that both the orthonormality of wave functions and the decay of the total energy can be preserved well by this linear scheme, while a significant acceleration can be observed from the numerical experiments due to the removal of an iteration process in the nonlinear scheme. The second one is the introduction of the adaptivity in the algorithm both temporally and spatially -i.e. an h-adaptive mesh method is employed to control the total amount of mesh grids, and an adaptive stop criterion in time propagation process is designed based on an observation that total energy always decays much faster at the beginning. Plenty of numerical experiments successfully demonstrate effectiveness of our method.

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Section: Introductionmentioning

confidence: 99%

A Linearized Structure-Preserving Numerical Scheme for a Gradient Flow Model of the Kohn-Sham Density Functional Theory

Hu¹,

Zhou²

2023

EAJAM

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“…Thus, concerned with the efficiency and the parallel scalability, an orthogonalization-free model is needed towards the simulation of large scale system. It is worth mentioning that in [16], an infeasible approach has been proposed based on the finite element method for calculating the ground state, which successfully removed the orthogonalization operation in the simulation.…”

Section: Introductionmentioning

confidence: 99%

A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

Guanghui Hu,

Yedan Shen,

Ting Wang

et al. 2023

NMTMA

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In [Dai et al., Multi. Model. Simul. 18(4) (2020)], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu et al., EAJAM. 13(2) (2023)] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the h-adaptive mesh method is demonstrated following [Chen et al., Multi. Model. Simul. 12 (2014)], with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model. Numerical examples confirm the theoretical results very well.

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“…Despite the simplicity, the (A)BB stepsizes turn out to be significant benefits in solving various optimization problems. The most related application goes to solving KS equations as orthogonality constrained optimization problems, where the (A)BB stepsizes play as important local acceleration components; see, e.g., [23][24][25][26][27]. However, the application of the (A)BB stepsizes on the atomic structure relaxation problem remains to be investigated.…”

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confidence: 99%

A force-based gradient descent method for $\mathit{\text{ab initio}}$ atomic structure relaxation

Hu,

Gao,

Zhao

et al. 2022

Preprint

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An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory

Cited by 6 publications

References 47 publications

A Linearized Structure-Preserving Numerical Scheme for a Gradient Flow Model of the Kohn-Sham Density Functional Theory

A Linearized Structure-Preserving Numerical Scheme for a Gradient Flow Model of the Kohn-Sham Density Functional Theory

A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

A force-based gradient descent method for $\mathit{\text{ab initio}}$ atomic structure relaxation

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