Augmented Lagrangian formulation of orbitalfree density functional theory
Abstract
We present an Augmented Lagrangian formulation and its realspace implementation for nonperiodic OrbitalFree Density Functional Theory (OFDFT) calculations. In particular, we rewrite the constrained minimization problem of OFDFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higherorder finitedifferences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higherorder finitedifferences represent a computationally efficient discretization for performing OFDFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing planewave methods.
 Authors:
 Publication Date:
 OSTI Identifier:
 22382133
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 275; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; COMPARATIVE EVALUATIONS; DENSITY FUNCTIONAL METHOD; IMPLEMENTATION; KINETIC ENERGY; LAGRANGIAN FUNCTION; LIMITING VALUES; MINIMIZATION; PERIODICITY; SPACE; WAVE PROPAGATION
Citation Formats
Suryanarayana, Phanish, Email: phanish.suryanarayana@ce.gatech.edu, and Phanish, Deepa. Augmented Lagrangian formulation of orbitalfree density functional theory. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.07.006.
Suryanarayana, Phanish, Email: phanish.suryanarayana@ce.gatech.edu, & Phanish, Deepa. Augmented Lagrangian formulation of orbitalfree density functional theory. United States. doi:10.1016/J.JCP.2014.07.006.
Suryanarayana, Phanish, Email: phanish.suryanarayana@ce.gatech.edu, and Phanish, Deepa. Wed .
"Augmented Lagrangian formulation of orbitalfree density functional theory". United States.
doi:10.1016/J.JCP.2014.07.006.
@article{osti_22382133,
title = {Augmented Lagrangian formulation of orbitalfree density functional theory},
author = {Suryanarayana, Phanish, Email: phanish.suryanarayana@ce.gatech.edu and Phanish, Deepa},
abstractNote = {We present an Augmented Lagrangian formulation and its realspace implementation for nonperiodic OrbitalFree Density Functional Theory (OFDFT) calculations. In particular, we rewrite the constrained minimization problem of OFDFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higherorder finitedifferences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higherorder finitedifferences represent a computationally efficient discretization for performing OFDFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing planewave methods.},
doi = {10.1016/J.JCP.2014.07.006},
journal = {Journal of Computational Physics},
number = ,
volume = 275,
place = {United States},
year = {Wed Oct 15 00:00:00 EDT 2014},
month = {Wed Oct 15 00:00:00 EDT 2014}
}

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