A Kohn-Sham equation solver based on hexahedral finite elements

Authors:
Jun Fang;Xingyu Gao;Aihui Zhou
Affiliations:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Graduate Unive ...;HPCC, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Journal of Computational Physics
Year:
2012

Citing 6
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Abstract

We design a Kohn-Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C"6"0, C"1"2"0, and C"2"7"5H"1"7"2. It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.