  Spatially distributed problems are often approximately modelled in terms of
partial differential equations (PDEs) for appropriate coarse-grained quantities
(e.g. concentrations). The derivation of accurate such PDEs starting from finer
scale, atomistic models, and using suitable averaging, is often a challenging
task; approximate PDEs are typically obtained through mathematical closure
procedures (e.g. mean-field approximations). In this paper, we show how such
approximate macroscopic PDEs can be exploited in constructing preconditioners
to accelerate stochastic simulations for spatially distributed particle-based
process models. We illustrate how such preconditioning can improve the
convergence of equation-free coarse-grained methods based on coarse
timesteppers. Our model problem is a stochastic reaction-diffusion model
capable of exhibiting Turing instabilities.
