无限维Hamilton系统稳态解的保结构算法  

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

作　　者：秦于越[1] 邓子辰[1,2] 胡伟鹏[1,2] 

机构地区：[1]西北工业大学工程力学系,西安710072 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《应用数学和力学》2014年第1期22-28,共7页Applied Mathematics and Mechanics

基　　金：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)~~

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.Based on Hamilton variational principle and Bridges＇ multi-symplectic integration theory, a new structure-preserving algorithm was proposed to simulate the steady-state solution to the complex infinite dimensional Hamilton system. With Zufiria＇ s Boussinesq-type equations as an example, the high-order partial differential equation describing the steady-state solution to the Zufn-ia model was rewritten into a symmetric form under the energy flux conservation law and momentum flux conservation law firstly; then the box scheme for the symmetric form was constructed to simulate the steady-state solution to the Zufiria model. The numerical results show that the box scheme can well simulate the steady-state solution to the Zufiria model while properly preserving the momentum flux conservation law.

关 键 词：无穷维HAMILTON系统 保结构 稳态解 动量通量 

分 类 号：O175.24[理学—数学]