留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

无限维Hamilton系统稳态解的保结构算法

秦于越 邓子辰 胡伟鹏

秦于越, 邓子辰, 胡伟鹏. 无限维Hamilton系统稳态解的保结构算法[J]. 应用数学和力学, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003
引用本文: 秦于越, 邓子辰, 胡伟鹏. 无限维Hamilton系统稳态解的保结构算法[J]. 应用数学和力学, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003
QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System[J]. Applied Mathematics and Mechanics, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003
Citation: QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System[J]. Applied Mathematics and Mechanics, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003

无限维Hamilton系统稳态解的保结构算法

doi: 10.3879/j.issn.1000-0887.2014.01.003
基金项目: 国家自然科学基金(11172239;11372252;11372253);高校博士点基金(20106102110019;20126102110023);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802;GZ1312)
详细信息
    作者简介:

    秦于越(1980—),女,重庆人,博士生(E-mail: 769482448@qq.com);

  • 中图分类号: O175.24

Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

Funds: The National Natural Science Foundation of China(11172239;11372252;11372253)
  • 摘要: 基于Hamilton变分原理和Bridges意义下的多辛积分理论,提出了保持无穷维Hamilton系统稳态解能流通量和动量通量的保结构分析方法.针对复杂的无穷维Hamilton系统的多辛对称形式,首先讨论了其稳态解所满足的对称形式的守恒律问题;随后,以一个典型的无穷维Hamilton系统——Zufiria方程为例,采用box离散格式,模拟了其稳态解,并验证了算法的保结构性能.研究结果显示:采用保结构算法能够较好地模拟无穷维Hamilton系统的稳态解,并保持了无穷维Hamilton系统稳态解的能流通量和动量通量两个重要力学参量.这一研究结果将为复杂无穷维Hamilton系统稳态解的数值分析提供新的途径.
  • [1] FENG Kang. On difference schemes and symplectic geometry[C]// Proceeding of the 1984 Beijing Symposium on Differential Geometry and Differential Equations.Beijing: Science Press, 1985: 42-58.
    [2] ZHANG Su-ying, DENG Zi-chen, LI Wen-cheng. A precise Runge-Kutta integration and its application for solving nonlinear dynamical systems[J]. Applied Mathematics and Computation,2007,184(2): 496-502.
    [3] Bridges T J. Multi-symplectic structures and wave propagation[J]. Mathematical Proceedings of the Cambridge Philosophical Society,1997,121(1): 147-190.
    [4] Marsden J E, Shkoller S. Multisymplectic geometry, covariant Hamiltonians, and water waves[J]. Mathematical Proceedings of the Cambridge Philosophical Society,1999,125(3): 553-575.
    [5] HU Wei-peng, DENG Zi-chen, HAN Song-mei, ZHANG Wen-rong. Generalized multi-symplectic integrators for a class of Hamiltonian nonlinear wave PDEs[J]. Journal of Computational Physics,2013,235: 394-406.
    [6] HU Wei-peng, DENG Zi-chen, HAN Song-mei. An implicit difference scheme focusing on the local conservation properties for Burgers equation[J]. International Journal of Computational Methods,2012,9(2): 1240028.
    [7] Bridges T J, Donaldson N M. Secondary criticality of water waves—part 2: unsteadiness and the Benjamin-Feir instability from the viewpoint of hydraulics[J]. Journal of Fluid Mechanics,2006,565: 419-439.
    [8] Bridges T J, Donaldson N M. Secondary criticality of water waves—part 1: definition, bifurcation and solitary waves[J]. Journal of Fluid Mechanics,2006,565: 381-417.
    [9] Zufiria J A. Weakly nonlinear nonsymmetrical gravity waves on water of finite depth[J]. Journal of Fluid Mechanics,1987,180: 371-385.
    [10] Zufiria J A. Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth[J]. Journal of Fluid Mechanics,1987,184: 183-206.
  • 加载中
计量
  • 文章访问数:  1501
  • HTML全文浏览量:  165
  • PDF下载量:  1318
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-10-15
  • 修回日期:  2013-10-22
  • 刊出日期:  2014-01-15

目录

    /

    返回文章
    返回