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An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation
Yedan Shen1; Yang Kuang1; Guanghui Hu1,2
2019-04
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume79Issue:1Pages:464–492
Abstract

In Radovitzky and Ortiz (Comput Methods Appl Mech Eng 172(1–4):203–240, 1999), an error estimation technique for nonlinear PDEs is presented to adaptively generating mesh, based on the reduction of the order of the approximate polynomial. In this paper, following a similar analysis framework, we propose an a posteriori error estimation for Kohn–Sham equation by coarsening mesh. An upper bound for the difference of the total energies on two successively refined meshes is derived by the numerical solutions on two meshes through an asymptotic analysis, which finally generates an a posteriori error estimation. A variety of numerical tests show that such an a posteriori error estimation works very well in our h-adaptive finite element method framework. In addition, to further improve the efficiency, we solve a Poisson equation instead of the Kohn–Sham equation on the coarsened mesh. The effectiveness of this improvement is analyzed and numerically examined.

KeywordElectronic Structure Calculation Coarsening Mesh Kohn–sham Density Functional Theory Adaptive Finite Element Method Ground State Energy
DOIhttps://doi.org/10.1007/s10915-018-0861-0
Language英语
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorGuanghui Hu
Affiliation1.Department of Mathematics, University of Macau, Macau, Macao SAR, China
2.Zhuhai UM Science and Technology Research Institute, Zhuhai, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Yedan Shen,Yang Kuang,Guanghui Hu. An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation[J]. Journal of Scientific Computing,2019,79(1):464–492.
APA Yedan Shen,Yang Kuang,&Guanghui Hu.(2019).An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation.Journal of Scientific Computing,79(1),464–492.
MLA Yedan Shen,et al."An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation".Journal of Scientific Computing 79.1(2019):464–492.
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