High Order Compact Splitting Multisymplectic Schemes for 1D Gross-Pitaevskii Equation

doi:10.19596/j.cnki.1001-246x.7748

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2018, Vol. 35 ›› Issue (6): 657-667.DOI: 10.19596/j.cnki.1001-246x.7748

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High Order Compact Splitting Multisymplectic Schemes for 1D Gross-Pitaevskii Equation

FU Fangfang¹, KONG Linghua², WANG Lan^2,3, XU Yuan², ZENG Zhankuan²

1. Department of Fundamental Education, Nanchang Institute of Science & Technology, Nanchang Jiangxi 330108, China;
2. College of Mathematics and Information, Jiangxi Normal University, Nanchang Jiangxi 330022, China;
3. Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Received:2017-08-29 Revised:2017-11-07 Online:2018-11-25 Published:2018-11-25
Supported by:
Supported by the NNSFC (11301234, 11271171,11501082), the Natural Science Foundation of Jiangxi Province (20161ACB20006, 20142BCB23009, 20181BAB201008)

Abstract

Abstract: We construct two high order compact schemes for 1D Gross-Pitaevskii (GP) equation. These schemes possess properties of multi-symplectic integrators, splitting method and high order compact method. It improves greatly computational efficiency of multisymplectic integrators. Firstly, 1D GP equation is reformulated into multisymplectic formulation. Then, it is split into a linear multisymplectic Hamiltonian and a nonlinear Hamiltonian system. The nonlinear sub-problem can be solved exactly based on new pointwise mass conservation law. The linear problem is discretized by high order compact multi-symplectic integrator. With different composition of the two sub-problems, we obtain two numerical schemes. These schemes have characters of multisymplectic integrators, splitting method and high order compact schemes, and they are mass-preserving as well. Numerical results are reported to illustrate performance of our methods.

Key words: Gross-Pitaevskii equation, splitting method, high order compact method, multisymplectic Hamiltonian system, multisymplectic integrator

CLC Number:

O241.8

FU Fangfang, KONG Linghua, WANG Lan, XU Yuan, ZENG Zhankuan. High Order Compact Splitting Multisymplectic Schemes for 1D Gross-Pitaevskii Equation[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(6): 657-667.

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High Order Compact Splitting Multisymplectic Schemes for 1D Gross-Pitaevskii Equation

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