Journal
MULTISCALE MODELING & SIMULATION
Volume 12, Issue 4, Pages 1828-1869Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130916096
Keywords
Kohn-Sham density functional theory; nonlinear eigenvalue problem; adaptive finite element approximation; convergence; complexity
Funding
- Funds for Creative Research Groups of China [11321061]
- National Basic Research Program of China [2011CB309703]
- National Science Foundation of China [11101416, 91330202]
- National 863 Project of China [2012AA01A309]
- National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences
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The Kohn-Sham model is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanoscience. In this paper, we study adaptive finite element approximations for the Kohn-Sham model. Based on the residual-type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using a Dorfler marking strategy, we then get the convergence rate and quasi-optimal complexity. Moreover, we demonstrate several typical numerical experiments that not only support our theory, but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.
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