摘要
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 fi-nite 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.
基金
Thework ofG.Baowas supported in part by the NSF grantsDMS-0968360,DMS-1211292
the ONR grant N00014-12-1-0319
a Key Project of the Major Research Plan of NSFC(No.91130004)
a special research grant from Zhejiang University
The research of G.H.Hu was supported in part by MYRG2014-00111-FST and MRG/016/HGH/2013/FST from University of Macao,085/2012/A3 from FDCT of Macao S.A.R.,and National Nat-ural Science Foundation of China(Grant No.11401608)
The research of D.Liu was supported by NSF grants DMS-0968360 and NSF-DMS 1418959.
