连续时间系统二维不稳定流形的异构算法

李清都; 谭宇玲; 杨芳艳

doi:10.7498/aps.60.030206

摘要

非线性系统的二维流形通常具有复杂几何结构和丰富动力学信息,因此在流形计算与可视化时存在大量的不可避免的数值计算.因此,如何高效地完成这些计算就成了关键问题.鉴于当今计算机的异构发展趋势(包含多核CPU和通用GPU),本文在兼顾精度和通用性的基础上,提出了适用于新一代计算平台的快速流形计算方法.本算法将计算任务分为轨道延伸和三角形生成两部分,前者运算量大而单一适合GPU完成,后者运算量小而复杂适合CPU执行.通过对Lorenz系统原点稳定流形的计算,表明本算法能充分发挥异构平台的综合性能,可大幅度提高计算速

关键词:

Abstract

Two-dimensional manifolds usually contain many nonlinear behaviors in complicate structures, which implies that much numerical calculation must be done during computing. Therefore, how to accomplish the work efficiently is a key problem. Since today’s computers tend to heterogeneous platforms including multi-core CPUs and general purpose GPUs, this paper proposes a fast manifold computing algorithm, which is not only of high precision and versatility, but also very suited to the new generation of computers. The algorithm contains two kinds of computation: extending trajectories and generating triangles. The former is large and simple, which is suitable for GPU; the later is small and complicate, which is suitable for CPU. The computation for the stable manifold of the Lorenz system at the origin shows that this algorithm ensures the best performance of heterogeneous platforms and improve the computing speed greatly.

Keywords:

作者及机构信息

(1)重庆邮电大学非线性系统研究所,重庆 400065; (2)重庆邮电大学网络化控制与智能仪器仪表教育部重点实验室,重庆 400065

基金项目: 国家自然科学基金(批准号:10926072,10972082),重庆市教委项目(批准号:KJ080515),重庆市科委项目(批准号:CSTC-2008BB2409)资助的课题.

Authors and contacts

(1)Institute for Nonlinear Systems, Chongqing Univ. Posts and Telecommunications, Chongqing 400065, China; (2)Key Laboratory of Network Control & Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

参考文献

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[3]	Guckenheimer J, Vladimirsky A A 2004 SIAM J Appli. Dyn. Sys. 3 232
[4]	Henderson M 2005 SIAM Journal on Applied Dynamical Systems 4 832
[5]	Krauskopf B, Osinga H 2005 Int. J. Bifurcation and Chaos 15 763
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[8]	Kirk D, Hwu W 2010 Programming Massively Parallel Processors (Burlington: Elsevier)
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[10]	Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese) [李丽香、彭海朋、杨义先、王向东 2007 56 51]
[11]	Gao F, Li Z Q, Tong H Q 2008 Chin. Phys. B 17 1196
[12]	Zheng Y, Zhang X D 2010 Chin. Phys. B 19 010505
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[14]	Li S H, Tian Y P 2003 Chin. Phys. 12 590
[15]	Niu Y J, Xu W, Rong H W,Wang L, Feng J Q 2009 Acta Phys. Sin. 58 2983 (in Chinese)
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[17]	Giuseppe G 2008 Chin. Phys. B 17 3247
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[21]	Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
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施引文献

[1]	Doedel E J, Champneys A R 1997 ftp://ftp.cs.concordia.ca/pub/doedel/auto/
[2]	Krauskopf B, Osinga H M 2003 SIAM J. Appl. Dyn. Sys. 2 546
[3]	Guckenheimer J, Vladimirsky A A 2004 SIAM J Appli. Dyn. Sys. 3 232
[4]	Henderson M 2005 SIAM Journal on Applied Dynamical Systems 4 832
[5]	Krauskopf B, Osinga H 2005 Int. J. Bifurcation and Chaos 15 763
[6]	Li Q D, Yang X S 2005 Computational Physics 22 549 (in Chinese) [李清都、杨晓松2005计算物理22 549]
[7]	Li Q D, Yang X S 2010 Acta Phys. Sin. 59 1416(in Chinese) [李清都、杨晓松 2010 59 1416]
[8]	Kirk D, Hwu W 2010 Programming Massively Parallel Processors (Burlington: Elsevier)
[9]	He W P, Feng G L, Gao X Q, Chou J F 2006 Acta Phys。 Sin. 55 3175 (in Chinese) [何文平、封国林、高新全、丑纪范 2006 55 3175]
[10]	Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese) [李丽香、彭海朋、杨义先、王向东 2007 56 51]
[11]	Gao F, Li Z Q, Tong H Q 2008 Chin. Phys. B 17 1196
[12]	Zheng Y, Zhang X D 2010 Chin. Phys. B 19 010505
[13]	Yu J Z, Su N, Vincent T L 1998 Acta Phys. Sin. 47 397 (in Chinese) [余建祖 1998 47 397]
[14]	Li S H, Tian Y P 2003 Chin. Phys. 12 590
[15]	Niu Y J, Xu W, Rong H W,Wang L, Feng J Q 2009 Acta Phys. Sin. 58 2983 (in Chinese)
[16]	Li X J Xu Z Y Xie Q C Wang B 2010 Acta Phys. Sin. 59 1532 (in Chinese) [李小娟、徐振源、谢青春、王兵 2010 59 1532]
[17]	Giuseppe G 2008 Chin. Phys. B 17 3247
[18]	Chen G P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平、郝加波 2009 58 2914]
[19]	Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元、王明军 2007 56 5136]
[20]	Han X J, Jiang B, Bi Q S 2009 Acta Phys. Sin. 58 6006 (in Chinese) [韩修静、江波、毕勤胜 2009 58 6006]
[21]	Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[22]	Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬、胡建兵、刘旭辉 2010 59 2305]
[23]	Cang S J, Chen Z Q, Wu W J 2009 Chin. Phys. B 18 1792
[24]	Wang G Y, Zheng Y, Liu J B 2007 Acta Phys. Sin. 56 3113 (in Chinese) [王光义、郑艳、刘敬彪 2007 56 3113]
[25]	Hao J H, Sun Z H, Xu H B 2007 Acta Phys. Sin. 56 6857 (in Chinese) [郝建红、孙志华、许海波 2007 56 6857]

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