Non-periodic finite-element formulation of Kohn–Sham density functional theory
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.
© 2009 Elsevier Ltd. Received 26 January 2009; revised 10 July 2009; accepted 6 October 2009; available online 16 October 2009. We gratefully acknowledge the support of the US Department of Energy through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials. V.G. also gratefully acknowledges the support of the Air Force Office of Scientific Research under Grant no. FA9550-09-1-0240.