Preconditioning of self-consistent-field cycles in density-functional theory: The extrapolar method

Anglade, Pierre-Matthieu; Gonze, Xavier

doi:10.1103/physrevb.78.045126

Cited by 34 publications

(54 citation statements)

References 26 publications

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“…Yet it yields an unfavorable scaling with system size together with a large prefactor that makes it virtually unusable on a planewave basis for systems with more than about ten atoms. The extrapolar [173] method is an approximate of this method that allows a dramatic reduction of the prefactor while almost preserving its perfect preconditioner behaviour.…”

Section: The Extrapolar Methods For Self-consistent Cycles Backgroundmentioning

confidence: 99%

ABINIT: First-principles approach to material and nanosystem properties

Gonze

Amadon

Anglade

et al. 2009

Computer Physics Communications

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Section: The Extrapolar Methods For Self-consistent Cycles Backgroundmentioning

confidence: 99%

ABINIT: First-principles approach to material and nanosystem properties

Gonze

Amadon

Anglade

et al. 2009

Computer Physics Communications

Self Cite

2,476

1,603

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“…These include Pulay's Direct Inversion in the Iterative Subspace (DIIS) method [6] and its variants [7,8], Broyden's quasi-Newton technique [9,10] and its variations [11][12][13][14], the Relaxed Constrained Algorithm (RCA) [15,16], and a variety of preconditioning schemes [5,[17][18][19][20]. Among these, Pulay's DIIS mixing schemebased on the extrapolation method of Anderson [21] -has enjoyed considerable popularity and success due to its relative simplicity and overall performance [22].…”

Section: Introductionmentioning

confidence: 98%

Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations

Pratapa

Suryanarayana

2015

Chemical Physics Letters

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a b s t r a c tWe present a variant of the restarted Pulay's Direct Inversion in the Iterative Subspace (DIIS) method for efficiently and robustly accelerating the convergence of fixed-point iterations. Specifically, we propose a simple modification of DIIS without any additional parameters, which we refer to as the r-Pulay method. We demonstrate the efficacy of r-Pulay in the context of the Jacobi iteration for solving large linear systems of equations, as well as in the Self Consistent Field (SCF) approach for Density Functional Theory (DFT) calculations. Overall, we find r-Pulay to be an attractive version of the restarted DIIS method.

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“…As Ref. [79] notes, even in situations whereby the density vanishes in some region, meaning that negative powers of the density are divergent, the linear response function tempers this divergence, and the exchangecorrelation contribution remains well-conditioned.…”

Section: H Ill-conditioning and Charge Sloshingmentioning

confidence: 99%

Computing the self-consistent field in Kohn–Sham density functional theory

Woods

Payne

Hasnip

2019

J. Phys.: Condens. Matter

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A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory. The aims of this work are two-fold. First, we explore the properties of Kohn-Sham density functional theory as it pertains to the convergence of selfconsistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the scf-xn suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner. CONTENTS

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Preconditioning of self-consistent-field cycles in density-functional theory: The extrapolar method

Cited by 34 publications

References 26 publications

ABINIT: First-principles approach to material and nanosystem properties

ABINIT: First-principles approach to material and nanosystem properties

Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations

Computing the self-consistent field in Kohn–Sham density functional theory

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