Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 61, Issue 1, Pages 38-60Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2012.09.002
Keywords
Density Functional Theory; Coarse-graining; Defects; Linear-scaling; Gauss quadrature
Funding
- US Army Research Office (under MURI) [W911NF-07-1-0410]
- US Department of Energy National Nuclear Security Administration through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials [DE-FC52-08NA28613]
- US National Science Foundation (under PIRE) [OISE-0967140]
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We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples. (C) 2012 Elsevier Ltd. All rights reserved.
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