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Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation

Part of: Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  15 January 2016

Gang Bao ,
Guanghui Hu  and
Di Liu
Gang Bao
Affiliation:
Department of Mathematics, Zhejiang University, Hang Zhou, Zhejiang Province, China
Guanghui Hu*
Affiliation:
Department of Mathematics, University of Macau, Macao S.A.R., China UM Zhuhai Research Institute, Zhuhai, Guangdong Province, China
Di Liu
Affiliation:
Department of Mathematics, Michigan State University, Michigan, USA
*
*Corresponding author. Email addresses:baog@zju.edu.cn (G. Bao), garyhu@umac.mo (G. H. Hu), richardl@math.msu.edu (D. Liu)
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Abstract

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, An h-adaptive finite element solver for the calculations of the electronic structures, 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.

Keywords

Translational invarianceadaptive finite element methodsKohn-Sham equationunstructured mesh

MSC classification

Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger) 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 1 , January 2016 , pp. 1 - 23
Copyright
Copyright © Global-Science Press 2016 

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