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Hu, Guanghui; Xie, Hehu; Xu, Fei

A multilevel correction adaptive finite element method for Kohn-Sham equation. (English) Zbl 1380.65371

J. Comput. Phys. 355, 436-449 (2018).
Summary: In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Cited in 1 Review
Cited in 21 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Z05 Applications to the sciences
81V45 Atomic physics

Keywords:

density functional theory; Kohn-Sham equation; multilevel correction; adaptive finite element method

Software:

KSSOLV
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Full Text: DOI

References:

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