Journal of Scientific Computing

, Volume 55, Issue 2, pp 372–391

Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique


DOI: 10.1007/s10915-012-9636-1

Cite this article as:
Bao, G., Hu, G. & Liu, D. J Sci Comput (2013) 55: 372. doi:10.1007/s10915-012-9636-1


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.


Adaptive mesh redistribution Harmonic map Finite element method Kohn-Sham equation Density functional theory 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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