Suryanarayana, Phanish and Bhattacharya, Kaushik and Ortiz, Michael (2013) Coarse-graining Kohn–Sham Density Functional Theory. Journal of the Mechanics and Physics of Solids, 61 (1). pp. 38-60. ISSN 0022-5096. http://resolver.caltech.edu/CaltechAUTHORS:20121204-074348348
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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.
|Additional Information:||© 2012 Elsevier Ltd. Received 8 December 2011. Received in revised form 27 July 2012. Accepted 1 September 2012. Available online 17 September 2012. Dedicated to Richard D.James on his sixtieth birthday. This work draws from the thesis of PS at the California Institute of Technology. We gratefully acknowledge the support of the US Army Research Office (under MURI Grant number W911NF-07-1-0410), the US Department of Energy National Nuclear Security Administration (under Award Number DE-FC52-08NA28613 through Caltech’s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials) and the US National Science Foundation (under PIRE Grant number OISE-0967140).|
|Subject Keywords:||Density Functional Theory; Coarse-graining; Defects; Linear-scaling; Gauss quadrature|
|Official Citation:||Phanish Suryanarayana, Kaushik Bhattacharya, Michael Ortiz, Coarse-graining Kohn–Sham Density Functional Theory, Journal of the Mechanics and Physics of Solids, Volume 61, Issue 1, January 2013, Pages 38-60, ISSN 0022-5096, 10.1016/j.jmps.2012.09.002. (http://www.sciencedirect.com/science/article/pii/S0022509612001949)|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||04 Dec 2012 16:21|
|Last Modified:||23 Aug 2016 10:22|
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