| 非线性Schrdinger方程的保辛数值求解 |
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| 引用本文： | 孙雁,高强,钟万勰.非线性Schrdinger方程的保辛数值求解[J].计算力学学报,2015,32(5):595-600,607. |
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| 作者姓名： | 孙雁 高强 钟万勰 |
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| 作者单位： | 上海交通大学 船舶海洋与建筑工程学院 工程力学系, 上海 200240;大连理工大学 工业装备结构分析国家重点实验室 工程力学系, 大连 116024;上海交通大学 船舶海洋与建筑工程学院 工程力学系, 上海 200240;大连理工大学 工业装备结构分析国家重点实验室 工程力学系, 大连 116024 |
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| 基金项目： | 国家自然科学基金(51278298);国家863计划(2012AA022606)资助项目. |
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| 摘 要： | 首先将非线性Schrdinger方程化为Hamilton正则方程形式,而后建立Hamilton体系下的变分原理。再用有限元法离散空间坐标,同时对时间坐标进行精细积分,最后运用混合能变分原理,提出非线性Schrdinger方程保辛数值解法。这种解法在保辛的同时,可以让能量和质量在积分格点上亦全部达到守恒。数值算例验证了该方法的有效性。
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| 关 键 词： | 非线性Schrö dinger 方程 Hamilton体系 保辛 能量守恒 区段混合能 |
| 收稿时间： | 2014/6/21 0:00:00 |
| 修稿时间： | 2014/8/27 0:00:00 |
Numerical solution with symplectic preserving of nonlinear Schrödinger equation |
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| SUN Yan,GAO Qiang and ZHONG Wan-xie.Numerical solution with symplectic preserving of nonlinear Schrödinger equation[J].Chinese Journal of Computational Mechanics,2015,32(5):595-600,607. |
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| Authors: | SUN Yan GAO Qiang and ZHONG Wan-xie |
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| Institution: | Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | This paper proposes a new numerical method with symplectic preserving to nonlinear Schrödinger equation,and the validity of this method is proved by numerical examples.We firstly transform nonlinear Schrödinger equation to Hamilton equations and therefore found Hamilton variational principle,followed with the discrete space coordinate through finite element method,precise integration algorithm used on time coordinate,and then with the mixed-energy variational principle,a numerical symplectic-preserving solution of nonlinear Schrödinger equation in the paper is well presented,while energy and mass preserving is realized simultaneously on the integration grids.Numerical examples later on demonstrate the effectiveness of this method. |
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| Keywords: | nonlinear Schrö dinger equation Hamilton system symplectic preserving energy preserving interval mixed energy |
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