摘要
基于Hamilton空间体系的多辛理论研究了膜自由振动问题,讨论了构造复合离散多辛格式的方法,并构造了一种典型的9×3点半隐式的多辛复合离散格式,该格式满足多辛守恒律、能量守恒律和动量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.
The multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space were considered. The complex method was introduced and a semi-implicit twenty-seven-point scheme with certain discrete conservation laws- a multi-symplectic conservation law （CLS）,an energy conservation law （ECL） as well as a momentum conservation law （MCL） - is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent leng-time numerical behavior.
出处
《应用数学和力学》
CSCD
北大核心
2007年第9期1054-1062,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(1057211910632030)
教育部新世纪优秀人才计划资助项目(NCET-04-0958)
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资助项目
