期刊
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
卷 14, 期 1, 页码 219-241出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.111211.270712a
关键词
LOD-MS; Gross-Pitaevskii equation; local one-dimensional method; midpoint method; conservation laws
资金
- National Natural Science Foundation of China [10901074, 11271171, 11126118]
- Provincial Natural Science Foundation of Jiangxi [20114BAB201011]
- Foundation of Department of Education Jiangxi Province [GJJ12174]
- State Key Laboratory of Scientific and Engineering Computing, CAS
- Director Innovation Foundation of ICMSEC and AMSS
- Foundation of CAS
- NNSFC [91130003, 11021101]
- Special Funds for Major State Basic Research Projects of China [2005CB321701]
The local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrodinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrodinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.
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