Time‐steppers and ‘coarse’ control of distributed microscopic processes

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Abstract
We present an equation‐free multiscale computational framework for the design of ‘coarse’ controllers for complex spatially distributed processes described by microscopic/mesoscopic evolution rules. We illustrate this framework by designing discrete‐time, coarse linear controllers for a Lattice–Boltzmann (LB) scheme modelling a reaction–diffusion process (a kinetic‐theory based realization of the FitzHugh–Nagumo equation dynamics in one spatial dimension). Short ‘bursts’ of appropriately initialized simulation of the LB model are used to extract the stationary states (stable and unstable) and to estimate the information required to design the coarse controller (e.g. the action of the coarse slow Jacobian of the process). Copyright © 2004 John Wiley & Sons, Ltd.