@Article{CiCP-19-1,
author = {Gang Bao, Guanghui Hu and Di Liu},
title = {Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {1},
pages = {1--23},
abstract = {<p style="text-align: justify;">Numerical oscillation of the total energy can be observed when the Kohn-Sham
equation is solved by real-space methods to simulate the translational move of
an electronic system. Effectively remove or reduce the unphysical oscillation is crucial
not only for the optimization of the geometry of the electronic structure, but also for
the study of molecular dynamics. In this paper, we study such unphysical oscillation
based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, <em>An h-adaptive finite element solver for the calculations of the electronic structures</em>, Journal of Computational
Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numerical
methods to constrain such unphysical effect for both pseudopotential and all-electron
calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The
numerical results demonstrate the effectiveness of our method on restraining unphysical
oscillation of the total energies.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.190115.200715a},
url = {http://global-sci.org/intro/article_detail/cicp/11078.html}
}