Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 55, Issue 2, Pages 372-391Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-012-9636-1
Keywords
Adaptive mesh redistribution; Harmonic map; Finite element method; Kohn-Sham equation; Density functional theory
Categories
Funding
- NSF Focused Research Group [DMS-0968360]
- NSF [DMS-0968360, DMS-0908325, CCF-0830161, EAR-0724527, DMS-1211292]
- ONR [N00014-12-1-0319]
- Key Project of the Major Research Plan of NSFC [91130004]
- Zhejiang University
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0968360] Funding Source: National Science Foundation
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A mesh redistribution method is introduced to solve the Kohn-Sham equation. The standard linear finite element space is employed for the spatial discretization, and the self-consistent field iteration scheme is adopted for the derived nonlinear generalized eigenvalue problem. A mesh redistribution technique is used to optimize the distribution of the mesh grids according to wavefunctions obtained from the self-consistent iterations. After the mesh redistribution, important regions in the domain such as the vicinity of the nucleus, as well as the bonding between the atoms, may be resolved more effectively. Consequently, more accurate numerical results are obtained without increasing the number of mesh grids. Numerical experiments confirm the effectiveness and reliability of our method for a wide range of problems. The accuracy and efficiency of the method are also illustrated through examples.
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