时变向量场中特殊轨迹的计算

计算物理 ›› 2011, Vol. 28 ›› Issue (4): 611-620.

时变向量场中特殊轨迹的计算

孙恒义, 樊养余, 贾蒙, 李慧敏, 张菁

西北工业大学电子信息学院, 陕西西安 710129

收稿日期:2010-05-26 修回日期:2010-12-05 出版日期:2011-07-25 发布日期:2011-07-25
作者简介:孙恒义(1985-),男,河北石家庄,硕士,从事数字信号处理研究,西北工业大学长安校区117信箱710129,E-mail:sunnyfly@mail.nwpu.edu.cn
基金资助:
基于网格法及Foliation条件机理的非线性向量场高维流形计算研究(项目号:60872159)资助项目

Computation of Distinguished Trajectories in Time Dependent Vector Fields

SUN Hengyi, FAN Yangyu, JIA Meng, LI Huimin, ZHANG Jing

School of Electronic Information of Northwestern Polytechnical University, Xi'an 710129, China

Received:2010-05-26 Revised:2010-12-05 Online:2011-07-25 Published:2011-07-25

摘要/Abstract

摘要： 通过考察特殊双曲轨迹的定义和已有的相空间度量函数,给出在扩展相空间中的度量函数.由于已有算法在计算过程中保持精度不变,造成对于高精度要求的情况计算量大,收敛效率低,故提出一种变步长收敛算法.利用瞬时驻点轨迹估计数值计算的初始区域,采用变步长网格提高计算效率.经过理论推导和实验分析,给出关键参数的最优取值范围.在二维和三维达芬系统上进行测试.实验表明,扩展相空间中的度量函数具有更好的平滑收敛性和稳定性;变步长收敛算法对于高精度计算具有高效性.

关键词: 非自治系统, 时变向量场, 特殊轨迹

Abstract: With definition of DHT(distinguished hyperbolic trajectory) and existing measure function in phase space,a measure function in extended phase space is presented.Existing algorithms with constant accuracy parameters is laborious as high precision is required.In order to overcome this shortage,a variable-step convergence algorithm is proposed.The main idea is to estimate initial region with the help of ISP(instantaneous stagnation points) and adopt variable-step grids to increase efficiency.With theoretical analysis and numerical calculation,an optimal range of key parameter is given.Two-dimensional and three-dimensional Duffing systems are used to test the performance.It shows that convergence route gained by the developed measure function is smooth and stable.And the variable-step convergence algorithm is more efficient.

Key words: non-autonomous system, time dependent vector fields, distinguished trajectory

中图分类号:

O193

孙恒义, 樊养余, 贾蒙, 李慧敏, 张菁. 时变向量场中特殊轨迹的计算[J]. 计算物理, 2011, 28(4): 611-620.

SUN Hengyi, FAN Yangyu, JIA Meng, LI Huimin, ZHANG Jing. Computation of Distinguished Trajectories in Time Dependent Vector Fields[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(4): 611-620.