This equation-free toolbox empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to use microscopic simulators to perform system level tasks and analysis, because microscale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing only short bursts of of the microscale simulator, and often only computing on small patches of the spatial domain. This suite of functions empowers users to start implementing such methods in their own applications. The document eqnFreeUserMan.pdf describes how to use the main functions of interest to you.
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The above graph illustrates an `equation-free' computation on only small well-separated patches of the spatial domain. The micro-scale simulations within each patch, here a nonlinear diffusive system, are craftily coupled to neighbouring patches and thus interact to provide accurate macro-scale predictions over the whole spatial domain. We have proved that the patches may be tiny, and still the scheme makes accurate macro-scale predictions. Thus the computational savings may be enormous, especially when combined with projective integration
Simulation over time is a complementary dynamic problem. The
`equation-free' approach is to simulate for only short
bursts of time, and then to extrapolate over un-simulated
time into the future, or into the past, or perform system
level analysis. This graph plots one example where the gaps
in time show the un-computed times between bursts of
computation.
By the way: Paul Petersik is also developing some equation-free projective integration, but in python, see https://github.com/pjpetersik/eqnfree