Cellular-automata models of natural processes, implementation on supercomputers

Conventional mathematical models based on differential calculus are sometimes not capable to simulate nonlinear dissipative processes on micro- or nano-level of resolution. This fact stimulates the development of new approaches to spatial dynamics simulation. Among them, cellular automata (CA) modeling is one of the promising methodologies, due to CA large simulation capability and compatibility with modern trends in supercomputer architecture. Although CA simulation is intensively studied and used in different fields, a few attention is paid to studying the parallel implementation peculiarities of large scale CA-models on supercomputers. Just this aspect of CA-simulation is the subject of the paper aiming to analyse CA-simulation methods adaptiveness to supercomputing implementation based on validity conditions requirements for different modes of CA operation. For this purpose, the concept of the operation mode well known for simple CA (having only one transition rule) is expanded for composed CA (containing many transition rules). The new concept determines a CA-transition rules execution order, which in turn determines the behavioral properties of CA-model and their influence on the simulation performance. The obtained results are illustrated by some examples, which show CA methods at work by simulating essentially nonlinear and dissipative processes: superposition of asynchronous CAs for simulation of water permeating through porous medium and parallel composition of two CAs simulating pattern formation on a heated plate. Basically, the paper generalizes CA computer simulation theoretical results and experience obtained by researchers from the Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences.