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A heterogeneous computing algorithm for two-dimensional unstable manifolds of time-continuous systems

Li Qing-Du Tan Yu-Ling Yang Fang-Yan

A heterogeneous computing algorithm for two-dimensional unstable manifolds of time-continuous systems

Li Qing-Du, Tan Yu-Ling, Yang Fang-Yan
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  • 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.
    • Funds:
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    Krauskopf B, Osinga H M 2003 SIAM J. Appl. Dyn. Sys. 2 546

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    Guckenheimer J, Vladimirsky A A 2004 SIAM J Appli. Dyn. Sys. 3 232

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    Henderson M 2005 SIAM Journal on Applied Dynamical Systems 4 832

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    Krauskopf B, Osinga H 2005 Int. J. Bifurcation and Chaos 15 763

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    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]

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    Li Q D, Yang X S 2010 Acta Phys. Sin. 59 1416(in Chinese) [李清都、杨晓松 2010 物理学报 59 1416]

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    Kirk D, Hwu W 2010 Programming Massively Parallel Processors (Burlington: Elsevier)

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    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 物理学报 55 3175]

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    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 物理学报 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 物理学报 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 物理学报 59 1532]

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    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 物理学报 58 2914]

    [19]

    Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元、王明军 2007 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 56 6857]

  • [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 58 2914]

    [19]

    Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元、王明军 2007 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 56 6857]

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Publishing process
  • Received Date:  12 May 2010
  • Accepted Date:  01 July 2010
  • Published Online:  15 March 2011

A heterogeneous computing algorithm for two-dimensional unstable manifolds of time-continuous systems

  • 1. (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

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.

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