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Six-dimensional basins of attraction computation on small clusters with semi-parallelized SCM method

  • Nemanja AndonovskiEmail author
  • Stefano Lenci
Article
  • 10 Downloads

Abstract

In modern engineering applications it is needed to determine the robustness of stable steady states, which depends on the shape and size of the associated basins of attraction. Once the basins are known, the quantitative measures can be computed by means of dynamical integrity tools and arguments. Those numerical techniques applied to strongly nonlinear systems, with six of more phase-space variables, demand considerable amounts of computing power, available only on High Performance Computing platforms. With the aim to minimize utilization of computer resources, we developed a software to adapt basin computations to small, affordable, clusters. It is based on Simple Cell Mapping method, modified to reduce the memory load, adjust integration time and overcome discretization discontinuities. Resource intensive part of computations is parallelized with Message Passing Interface and less demanding operations are kept serial, due to their inherit sequential nature. As intended, the program computes full six-dimensional basins of attraction at the adequate accuracy to distinguish compact parts of basins, but not to fully disclose fractalities or chaos. Disadvantages of the SCM method are addressed and the effectiveness of proposed solutions are demonstrated and discussed by the paradigmatic example composed of three coupled Duffing oscillators.

Keywords

Basin of attraction Global analysis Simple Cell Mapping 

List of acronyms

2D

Two-dimensional

3D

Three-dimensional

6D

Six-dimensional

BoA

Basins of attraction

CM

Cell mapping

CPA

Connecting post-processing algorithm

CPU

Central processing unit

CSCM

Clustered Simple Cell Mapping

DOF

Degree of Freedom

FCVDP

Forced coupled Van der Pol oscillators

FDO

Forced Duffing oscillators

GB

Giga-byte

GoS

Grid of Starts

GPU

Graphical processing unit

HPC

High Performance Computing

MPI

Message Passing Interface standard

NSSCM

Not So Simple Cell Mapping

OpenMP

Open multi-processing application programming interface

PSCM

Parallel Simple Cell Mapping

RAM

Random access memory

SCM

Simple cell mapping

Notes

Acknowledgements

Authors would like to thank to Franco Moglie, Polytechnic University of Marche, Ancona, Italy, Radu Serban and Dan Negrut, University of Wisconsin-Madison, USA, for help with HPC.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Polytechnic University of MarcheAnconaItaly

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