Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 58, Issue 2, Pages 256-280Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2009.10.002
Keywords
Finite-elements; Kohn-Sham; Density functional theory; Gamma-convergence
Funding
- US Department of Energy
- Air Force Office of Scientific Research [FA9550-09-1-0240]
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We present a real-space, non-periodic, finite-element formulation for Kohn-Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away. (C) 2009 Elsevier Ltd. All rights reserved.
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