Error investigations in complex automata models for reaction-diffusion systems

Abstract

Complex Automata (CxA) have been recently introduced as a paradigm to simulate multiscale systems as a collection of generalized Cellular Automata on different scales. We present a basic mathematical framework to investigate the behavior of a CxA model depending on scale separation and modeling choices. In particular, a simple CxA model for a reaction-diffusion system, based on the lattice Boltzmann method, will be formally analyzed. Theoretical error estimates will be derived and numerically validated. © 2008 Springer-Verlag Berlin Heidelberg.