Higher-order adaptive finite-element methods for Kohn-Sham density functional theory

@article{Motamarri2013HigherorderAF,
  title={Higher-order adaptive finite-element methods for Kohn-Sham density functional theory},
  author={Phani Motamarri and Michael R. Nowak and Kenneth W. Leiter and Jaroslaw Knap and Vikram Gavini},
  journal={J. Comput. Phys.},
  year={2013},
  volume={253},
  pages={308-343}
}

Real time time-dependent density functional theory using higher order finite-element methods

TLDR
This work develops an a priori mesh adaption technique, based on the semi-discrete error estimate on the time-dependent Kohn-Sham orbitals, to construct a close to optimal finite-element discretization, and demonstrates a staggering 100-fold reduction in the computational time afforded by higher-order finite-elements over linear finite-Elements.

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The accuracy, efficiency and parallel scalability of the proposed method on semiconducting and heavy-metallic systems of various sizes, with the largest system containing 8694 electrons, are demonstrated.

An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation

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An a posteriori error estimation for Kohn–Sham equation by coarsening mesh is proposed and an upper bound for the difference of the total energies on two successively refined meshes is derived by the numerical solutions on two meshes through an asymptotic analysis.
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