561a

Deriving accurate macroscopic evolution equations (e.g. Partial Differential Equations) from detailed individual-based models is often a challenging task. Introducing closure assumptions -based on mathematics, or smart heuristics- can result in approximately valid macroscopic equations. In this work we illustrate how such "approximately correct" PDEs can be used to assist coarse-grained numerical computations based on the equation-free framework. We observe that the convergence of equation-free multiscale fixed-point solvers (based on, for example, Newton-GMRES) can be significantly accelerated through preconditioning which exploits approximate closures. Our model problem is a one-dimensional stochastic reaction-diffusion system that can exhibit Turing instabilities. We compute its coarse-grained bifurcation diagram using both equation-free and equation-assisted algorithms; stable as well as unstable coarse-grained, spatially varying solutions are computed and their (coarse-grained) stability is quantified. We also discuss possible extensions of the approach beyond this prototype example to more complex stochastic pattern formation problems.

See more of #561 - Simulation and Control of Multiscale Systems II (10D00)

See more of Computing and Systems Technology Division

See more of The 2006 Annual Meeting

See more of Computing and Systems Technology Division

See more of The 2006 Annual Meeting