Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation

In this work, operator-compensation based high order methods are presented to solve the Gross-Pitaevskii equation modeling Bose-Einstein condensation (BEC). We begin with the high-order approximation to the Laplacian by the central finite difference method combined with operator-compensation techniq...

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Bibliographic Details
Published in:Applied numerical mathematics 2020-05, Vol.151, p.337-353
Main Authors: Li, Xiang-Gui, Cai, Yongyong, Wang, Pengde
Format: Article
Language:English
Subjects:
Conservation
Gross-Pitaevskii equation
High-order methods
Operator-compensation methods
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Summary:In this work, operator-compensation based high order methods are presented to solve the Gross-Pitaevskii equation modeling Bose-Einstein condensation (BEC). We begin with the high-order approximation to the Laplacian by the central finite difference method combined with operator-compensation technique, and the Crank-Nicolson and time-splitting methods are then proposed for the time discretization. We show that the Crank-Nicolson operator-compensation method keeps the mass and energy conservation, while the time-splitting operator-compensation method only conserves the mass. Then by extending the high-order operator-compensation methods for the first order derivative, the time-splitting finite difference method is developed to solve the Gross-Pitaevskii equation with an angular momentum rotation term. Numerical results are given to test accuracy and verify the conservation properties.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2020.01.004