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

In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorit...

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Bibliographic Details
Published in:Journal of computational physics Vol. 231; no. 14; pp. 4967 - 4979
Main Authors: Bao, Gang, Hu, Guanghui, Liu, Di
Format: Journal Article
Language:English
Published: Kidlington Elsevier Inc 20.05.2012
Elsevier
Subjects:
Algorithms
Blocking
Computational efficiency
Computational techniques
Density functional theory
Eigenvalues
Exact sciences and technology
Finite element method
h-Adaptive
Kohn–Sham equation
Mathematical analysis
Mathematical methods in physics
Optimization
Physics
Solvers
Finite element method
Density functional theory
h-Adaptive
Kohn–Sham equation
Tetrahedron
Pseudopotential
Digital simulation
Conjugate gradient methods
Adaptive method
Calculation methods
Algorithms
Multigrid
Density functional method
Eigenvalue problem
Calculation
Kohn―Sham equation
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.04.002