Multi-Symplectic Methods for Membrane Free Vibration Equation
-
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．
-
关键词:
- 多辛 /
- 复合离散 /
- Runge-Kutta方法
Abstract: 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 lawsa 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 long-time numerical behavior.-
Key words:
- multi-symplectic /
- complex discretization /
- Runge-Kutta method
-
[1] Bridge T J, Reich S.Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity[J].Phys Lett A,2001,284(4/5):184-193. doi: 10.1016/S0375-9601(01)00294-8 [2] Moore B E, Reich S.Multi-symplectic integration methods for Hamiltonian PDEs[J].Future Generation Computer Systems,2003,19(3):395-402. doi: 10.1016/S0167-739X(02)00166-8 [3] Bridges T J. Multi-symplectic structures and wave propagation[J].Math Proc Camb Philos Soc,1997,121(1):147. doi: 10.1017/S0305004196001429 [4] Reich S. Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations[J].Computational Physics,2000,157(2):473-499. doi: 10.1006/jcph.1999.6372 [5] Izu Vaisman.Symplectic Geometry and Secondary Characteristic Classes[M]. Boston: Birkhuser, 1987. [6] 钟万勰. 应用力学的辛数学方法[M].北京:高等教育出版社,2006. [7] HONG Jia-lin, LI Chun.Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations[J].Computational Physics,2006,211(2):448-472. doi: 10.1016/j.jcp.2005.06.001 [8] SUN Jian-qiang, QIN Meng-zhao.Multi-symplectic methods for the coupled 1D nonlinear Schrdinger system[J].Computer Physics Communications,2003,155(3):221-235. doi: 10.1016/S0010-4655(03)00285-6 [9] Qin M Z, Zhang M Q. Multi-stage symplectic schemes of two kinds of Hamiltonian systems for wave equation[J].Comput Math Appl,1990,19(10):51. [10] Yoshida H. Construction of higher order symplectic integrators[J].Phys Lett A,1990,150(5/7):262-269. doi: 10.1016/0375-9601(90)90092-3 [11] 哈尔滨工业大学数学系组.数学物理方程[M].北京:科学出版社,2001. -
点击查看大图
计量
- 文章访问数: 2414
- HTML全文浏览量: 102
- PDF下载量: 714
- 被引次数: 0
下载:
