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An adaptive FEM with ITP approach for steady Schrodinger equation
Kuang, Yang1; Hu, Guanghui1,2

In this paper, an adaptive numerical method is proposed for solving a 2D Schrodinger equation with an imaginary time propagation approach. The differential equation is first transferred via a Wick rotation to a real time-dependent equation, whose solution corresponds to the ground state of a given system when time approaches infinity. The temporal equation is then discretized spatially via a finite element method, and temporally utilizing a Crank-Nicolson scheme. A moving mesh strategy based on harmonic maps is considered to eliminate possible singular behaviour of the solution. Several linear and nonlinear examples are tested by using our method. The experiments demonstrate clearly that our method provides an effective way to locate the ground state of the equations through underlying eigenvalue problems.

KeywordSchrodinger Equation Imaginary Time Propagation Moving Mesh Method Finite Element Method Ground State
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Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000428749300012
The Source to ArticleWOS
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
University of Macau
Affiliation1.Univ Macau, Fac Sci & Technol, Dept Math, Macau, Peoples R China
2.UM Zhuhai Res Inst, Zhuhai, Guangdong, Peoples R China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Kuang, Yang,Hu, Guanghui. An adaptive FEM with ITP approach for steady Schrodinger equation[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2018,95(1):187-201.
APA Kuang, Yang,&Hu, Guanghui.(2018).An adaptive FEM with ITP approach for steady Schrodinger equation.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,95(1),187-201.
MLA Kuang, Yang,et al."An adaptive FEM with ITP approach for steady Schrodinger equation".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 95.1(2018):187-201.
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