Abstract
In the paper, a systematic discussion is made of state of the art theory and applications of fine-grained (massive) parallelism, which is permanently being adopted in computational mathematics. All known models of fine-grained computations (cellular automaton, neural and cellular neural networks, statistical automata, etc.) are represented in terms of a unique formalism, the so-called parallel substitution algorithm (PSA), which made it possible, on the one hand, to highlight common properties of the models and, on the other hand, to demonstrate expressiveness capabilities of the PSA. Theoretical and experimental results of studies on applications of fine-grained algorithms to modeling of spatial dynamics of reaction–diffusion and molecular processes are presented. Promising prospects of their application are substantiated both for the creation of special processors designed for the implementation of the algorithms and for the implementation of the algorithms on multiprocessor systems.
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