一维Gross-Pitaevskii方程的高阶紧致分裂步多辛格式

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

计算物理 ›› 2018, Vol. 35 ›› Issue (6): 657-667.DOI: 10.19596/j.cnki.1001-246x.7748

一维Gross-Pitaevskii方程的高阶紧致分裂步多辛格式

符芳芳¹, 孔令华², 王兰^2,3, 徐远², 曾展宽²

1. 南昌工学院基础教育学院, 江西南昌 330108;
2. 江西师范大学数学与信息科学学院, 江西南昌 330022;
3. 南京师范大学数学科学院, 江苏省大规模复杂系统数值模拟重点实验室, 江苏南京 210023

收稿日期:2017-08-29 修回日期:2017-11-07 出版日期:2018-11-25 发布日期:2018-11-25
通讯作者: Kong Linghua (1977-),male,Ganzhou Jiangxi,professor,major in numerical methods for partial differential equations,E-mail:konglh@mail.ustc.edu
作者简介:YANG Longfei (1991-),male,master candidate,major in doped carbon materials and application in energy storage,E-mail:Yanglongfei24@163.com
基金资助:
Supported by the NNSFC (11301234, 11271171,11501082), the Natural Science Foundation of Jiangxi Province (20161ACB20006, 20142BCB23009, 20181BAB201008)

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)

摘要/Abstract

摘要： 首先把一维Gross-Pitaevskli方程改写成多辛Hamiltonian系统的形式，把形式通过分裂变成2个子哈密尔顿系统.然后，对这些子系统用辛或者多辛算法进行离散.通过对子系统数值算法的不同组合方式，得到不同精度的具有多辛算法特征数值格式.这些格式不仅具有多辛格式、分裂步方法和高阶紧致格式的特征，而且是质量守恒的.数值实验验证了新格式的数值行为.

关键词: Gross-Pitaevskii方程, 分裂步方法, 高阶紧致格式, 多辛哈密尔顿系统, 多辛格式

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

中图分类号:

O241.8

符芳芳, 孔令华, 王兰, 徐远, 曾展宽. 一维Gross-Pitaevskii方程的高阶紧致分裂步多辛格式[J]. 计算物理, 2018, 35(6): 657-667.

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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一维Gross-Pitaevskii方程的高阶紧致分裂步多辛格式

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

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