Error Investigations in Complex Automata Models for Reaction-Diffusion Systems

摘要

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.