Asymptotic analysis of Complex Automata models for reaction--diffusion systems

Authors:
Alfonso Caiazzo;Jean-Luc Falcone;Bastien Chopard;Alfons G. Hoekstra
Affiliations:
INRIA Rocquencourt, BP 105, F-78150 Le Chesnay Cedex, France;CUI Department, University of Geneva, Switzerland;CUI Department, University of Geneva, Switzerland;University of Amsterdam, Section Computational Science, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

Complex Automata (CxA) have been recently introduced as a paradigm to simulate multiscale multiscience systems as a collection of generalized Cellular Automata on different scales. The approach yields numerical and computational challenges and can become a powerful tool for the simulation of particular complex systems. We present a mathematical framework for CxA modeling to investigate the behavior of the model depending on scale separation and modeling choices. For a simple CxA model for a reaction-diffusion process, we define a Complex Automata model, deriving theoretical error estimates, which are numerically validated.