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A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation

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Abstract

The ‘equation-free toolbox’ empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable scientists and engineers to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because micro-scale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing the micro-scale simulator only over short bursts in time on small patches in space, with bursts and patches well-separated in time and space respectively. We introduce the suite of coded equation-free functions in an accessible way, link to more detailed descriptions, discuss their mathematical support, and introduce a novel and efficient algorithm for Projective Integration. Some facets of toolbox development of equation-free functions are then detailed. Download the toolbox functions and use to empower efficient and accurate simulation in a wide range of science and engineering problems.

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Notes

  1. https://github.com/uoa1184615/EquationFreeGit

  2. https://github.com/uoa1184615/EquationFreeGit

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Funding

This project is supported by the Australian Research Council via grants DP150102385 and DP180100050.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia, Australia

    John Maclean, J. E. Bunder & A. J. Roberts

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  1. John Maclean
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Correspondence to John Maclean.

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Maclean, J., Bunder, J.E. & Roberts, A.J. A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation. Numer Algor 87, 1729–1748 (2021). https://doi.org/10.1007/s11075-020-01027-z

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