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

作　　者：符芳芳[1] 孔令华[2] 王兰[2,3] 徐远 曾展宽[2] FU Fangfang;KONG Linghua;WANG Lan;XU Yuan;ZENG ghankuan(Department of Fundamental Education,Nanchang Institute of Science &Technology,Nanehang Jiangxi 330108,China;College of Mathematics and Information,Jiangxi Normal University,Nanchang Jiangxi 330022,China;Jiangsu Key Laboratory of NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)

机构地区：[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

出　　处：《计算物理》2018年第6期657-667,共11页Chinese Journal of Computational Physics

基　　金：Supported by the NNSFC(11301234,11271171,11501082);the Natural Science Foundation of Jiangxi Province(20161ACB20006,20142BCB23009,20181BAB201008)

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.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.

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 

分 类 号：O241.8[理学—计算数学]