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An adaptive FEM with ITP approach for steady Schrödinger equation
Kuang Y.2; Hu G.2
2018-01-02
Source PublicationInternational Journal of Computer Mathematics
ISSN10290265 00207160
Volume95Issue:1Pages:187-201
AbstractIn this paper, an adaptive numerical method is proposed for solving a 2D Schrödinger 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.
Keywordfinite element method ground state imaginary time propagation moving mesh method Schrödinger equation
DOI10.1080/00207160.2017.1366463
URLView the original
Language英語
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.UM Zhuhai Research Institute
2.Universidade de Macau
Recommended Citation
GB/T 7714
Kuang Y.,Hu G.. An adaptive FEM with ITP approach for steady Schrödinger equation[J]. International Journal of Computer Mathematics,2018,95(1):187-201.
APA Kuang Y.,&Hu G..(2018).An adaptive FEM with ITP approach for steady Schrödinger equation.International Journal of Computer Mathematics,95(1),187-201.
MLA Kuang Y.,et al."An adaptive FEM with ITP approach for steady Schrödinger equation".International Journal of Computer Mathematics 95.1(2018):187-201.
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