Abstract
Accuracy and stability properties of fine-grained parallel computations, based on modeling spatial dynamics by cellular automata (CA) evolution, are studied. The problem arises when phenomena under simulation are represented as a composition of a CA and a function given in real numbers, and the whole computation process is transferred into a Boolean domain. To approach the problem accuracy of real spatial functions approximation by Boolean arrays, as well as of some operations on cellular arrays with different data types are determined and approximation errors are assessed. Some methods of providing admissible accuracy are proposed. Stability is shown to depend only of the nonlinear terms in hybrid methods, the use of CA-diffusion instead of Laplace operator having no effect on it. Some experimental results supporting the theoretical conclusions are presented.
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References
von Neumann, J.: Theory of self reproducing automata. Uni. of Illinois, Urbana (1966)
Bandman, O.: Comparative Study of Cellular-Automata Diffusion Models. In: Malyshkin, V.E. (ed.) PaCT 1999. LNCS, vol. 1662, pp. 395–409. Springer, Heidelberg (1999)
Malinetski, G.G., Stepantsov, M.E.: Modeling Diffusive Processes by Cellular Automata with Margolus Neighborhood. Zhurnal Vychislitelnoy Matematiki i Matematicheskoy phiziki 36(6), 1017–1021 (1998)
Wolfram, S.: Cellular automata fluids 1: Basic Theory. Journ. Stat. Phys. 45, 471–526 (1986)
Rothman, D.H., Zaleski, S.: Lattice-Gas Cellular Automata. In: Simple models of complex hydrodynamics. Cambridge University Press, Cambridge (1997)
Vichniac, G.: Simulating Physics by Cellular Cellular Automata. Physica 10 D, 86–115 (1984)
Bandman, O.: Simulating Spatial Dynamics by Probabilistic Cellular Automata. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 10–19. Springer, Heidelberg (2002)
Bandman, O.: A Hybrid Approach to Reaction-Diffusion Processes Simulation. In: Malyshkin, V.E. (ed.) PaCT 2001. LNCS, vol. 2127, pp. 1–16. Springer, Heidelberg (2001)
Wolfram, S.: A new kind of Science. Wolfram media Inc., Champaign, Il. USA (2002)
Bandini, S., Mauri, G., Pavesi, G., Simone, C.: A Parallel Model Based on Cellular Automata for Simulation of Pesticide Percolation in the Soil. In: Malyshkin, V.E. (ed.) PaCT 1999. LNCS, vol. 1662, Springer, Heidelberg (1999)
Chua, L.: A Paradigm for Complexity. World Scientific, Singapore (1999)
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Bandman, O. (2003). Accuracy and Stability of Spatial Dynamics Simulation by Cellular Automata Evolution. In: Malyshkin, V.E. (eds) Parallel Computing Technologies. PaCT 2003. Lecture Notes in Computer Science, vol 2763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45145-7_3
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DOI: https://doi.org/10.1007/978-3-540-45145-7_3
Publisher Name: Springer, Berlin, Heidelberg
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