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Symplectic-like Difference Schemes for Generalized Hamiltonian Systems


doi: 10.1007/s00376-002-0011-2

  • The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.
  • [1] Liu Yangang, 1995: On the Generalized Theory of Atmospheric Particle Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 419-438.  doi: 10.1007/BF02657003
    [2] Jo-Han LEE, Dong-Kyou LEE, Hyun-Ha LEE, Yonghan CHOI, Hyung-Woo KIM, 2010: Radar Data Assimilation for the Simulation of Mesoscale Convective Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1025-1042.  doi: 10.1007/s00376-010-9162-8
    [3] Peng Jiayi, Wu Rongsheng, Wang Yuan, 2002: Initiation Mechanism of Meso-β Scale Convective Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 870-884.  doi: 10.1007/s00376-002-0052-6
    [4] Qiu Yongyan, Zhu Yafen, 1987: MEDIUM-RANGE OSCILLATIONS OF SYNOPTIC SYSTEMS IN SUMMER, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 395-402.  doi: 10.1007/BF02656740
    [5] ZHOU Lingli, ZHAI Guoqing, HE Bin, 2011: Numerical Study of the Mesoscale Systems in the Spiral Rainband of 0509 Typhoon Matsa, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 118-128.  doi: 10.1007/s00376-010-0023-2
    [6] LI Gang, HE Guangxin, Xiaolei ZOU*, and Peter Sawin RAY, 2014: A Velocity Dealiasing Scheme for C-band Weather Radar Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 17-26.  doi: 10.1007/s00376-013-2251-8
    [7] Na LI, Lingkun RAN, Linna ZHANG, Shouting GAO, 2017: Potential Deformation and Its Application to the Diagnosis of Heavy Precipitation in Mesoscale Convective Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 894-908.  doi: 10.1007/s00376-017-6282-4
    [8] Huw C. DAVIES, 2006: Large-Scale Weather Systems: A Future Research Priority, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 832-841.  doi: 10.1007/s00376-006-0832-5
    [9] GAO Shouting, TAN Zhemin, ZHAO Sixiong, LUO Zhexian, LU Hancheng, WANG Donghai, CUI Chunguang, CUI Xiaopeng, SUN Jianhua, 2015: Mesoscale Dynamics and Its Application in Torrential Rainfall Systems in China, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 192-205.  doi: 10.1007/s00376-014-0005-x
    [10] Xia Daqing, Zheng Liangjie, 1986: NUMERICAL SIMULATION OF THE GENERATION OF MESOSCALE CONVECTTVE SYSTEMS IN LARGE-SCALE ENVIRONMENT, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 360-370.  doi: 10.1007/BF02678656
    [11] Huan MEI, Faming WANG, Zhong ZENG, Zhouhua QIU, Linmao YIN, Liang LI, 2016: A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 377-390.  doi: 10.1007/s00376-015-5001-2
    [12] D. R. Chakraborty, P.S. Salvekar, 1989: An Efficient Accurate Direct Solution of Poisson’s Equation for Computation of Meteorological Parameters, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 501-508.  doi: 10.1007/BF02659084
    [13] Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 413-417.  doi: 10.1007/BF02919320
    [14] Daosheng XU, Dehui CHEN, Kaixin WU, 2021: Properties of High-Order Finite Difference Schemes and Idealized Numerical Testing, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 615-626.  doi: 10.1007/s00376-020-0130-7
    [15] WANG Pengfei, HUANG Gang, WANG Zaizhi, 2006: Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 758-766.  doi: 10.1007/s00376-006-0758-y
    [16] PENG Jie, ZHANG Hua, Zhanqing LI, 2014: Temporal and Spatial Variations of Global Deep Cloud Systems Based on CloudSat and CALIPSO Satellite Observations, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 593-603.  doi: 10.1007/s00376-013-3055-6
    [17] Chen Lianshou, Luo Zhexian, 2002: The Impact of the Eastward Shifting of Dipole Systems over Large-Scale Terrain on Tropical Cyclone Tracks, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 1069-1078.  doi: 10.1007/s00376-002-0065-1
    [18] ZHU Guofu, CHEN Shoujun, 2003: Analysis and Comparison of Mesoscale Convective Systems over the Qinghai-Xizang (Tibetan) Plateau, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 311-322.  doi: 10.1007/BF02690789
    [19] DONG Haiping, ZHAO Sixiong, ZENG Qingcun, 2007: A Study of Influencing Systems and Moisture Budget in a Heavy Rainfall in Low Latitude Plateau in China during Early Summer, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 485-502.  doi: 10.1007/s00376-007-0485-z
    [20] Zhiwei HE, Qinghong ZHANG, Jun SUN, 2016: The Contribution of Mesoscale Convective Systems to Intense Hourly Precipitation Events during the Warm Seasons over Central East China, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1233-1239.  doi: 10.1007/s00376-016-6034-x

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Manuscript History

Manuscript received: 10 July 2002
Manuscript revised: 10 July 2002
通讯作者: 陈斌, bchen63@163.com
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Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

  • 1. LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Institute of Science, PLA University of Science and Technology, Nanjing 211101,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

Abstract: The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.

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