Weakly coupled distributed calculation of Lyapunov exponents for non-linear dynamical systems

被引：1

作者：

Hernández-Gómez J.J. ^{[1
]}

Couder-Castañeda C. ^{[1
]}

Herrera-Díaz I.E. ^{[2
]}

Flores-Guzmán N. ^{[3
]}

Gómez-Cruz E. ^{[4
]}

机构：

[1] Centro de Desarrollo Aeroespacial, Instituto Politécnico Nacional, Ciudad de Mexico

[2] Departamento de Ingeniería Agroindustrial, Universidad de Guanajuato, Campus Celaya-Salvatierra, Celaya, Guanajuato

[3] Centro de Investigación en Matemáticas, Guanajuato, Guanajuato

[4] Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México

来源：

Algorithms | 2017年 / 10卷 / 04期

关键词：

Chaos theory; Distributed memory; Lyapunov exponents; MPI; Non-linear dynamical systems;

D O I：

10.3390/a10040137

中图分类号：

学科分类号：

摘要：

Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge-Kutta problems that need to be calculated. In this work we introduce a parallel implementation based on MPI (Message Passing Interface) for the calculation of the Lyapunov exponents for a multidimensional dynamical system, considering a weakly coupled algorithm. Since we work on an academic high-latency cluster interconnected with a gigabit switch, the design has to be oriented to reduce the number of messages required. With the design introduced in this work, the computing time is drastically reduced, and the obtained performance leads to close to optimal speed-up ratios. The implemented parallelisation allows us to carry out many experiments for the calculation of several Lyapunov exponents with a low-cost cluster. The numerical experiments showed a high scalability, which we showed with up to 68 cores. © 2017 by the authors.

引用

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