期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 275, 期 -, 页码 524-538出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.07.006
关键词
Augmented Lagrangian; Lagrange multiplier; Penalty; Higher-order finite-differences; Real-space; Non-periodic
资金
- National Science Foundation [1333500]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1333500] Funding Source: National Science Foundation
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT 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 higher-order finite-differences 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 higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT 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 plane-wave methods. (C) 2014 Elsevier Inc. All rights reserved.
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