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

Authors:
Gang Bao;Guanghui Hu;Di Liu
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China and Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

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.