Biology – Quantitative Biology – Quantitative Methods
Scientific paper
2006-06-07
Biology
Quantitative Biology
Quantitative Methods
8 pages, 6 figures, submitted to Journal of Chemical Physics
Scientific paper
10.1063/1.2372492
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.
Erban Radek
Kelley C. T.
Kevrekidis Ioannis G.
Qiao Liang
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