## Spatial functions approximation by Boolean arrays

Since Cellular Automata attract a growing interest as a model to be used in simulating spatial dynamics, the problem arises of Boolean data compatibility with continuous spatial functions widespread in physics. To solve this problem, a method to approximate real functions in discrete space by Boolean arrays and vice versa...

## Associative parallel algorithm performing depth-first search

In this paper, we propose a novel associative parallel algorithm performing depth-first search on an abstract model of the SIMD type with vertical data processing (the STAR-machine). This algorithm is represented in two ways: as recursive and non-recursive STAR procedures, whose correctness is verified and time complexity is evaluated.

## Simulation of the diffusion process by the residue number system

In this paper, computational potentialities of the residue number system for solution to the diffusion equation is investigated. The finite-difference diffusion scheme is modified in terms of the residue number system. Computer simulation has been performed. The computational characteristics (stability, accuracy) have been assessed and compared with similar ones obtained...

## The Godunov-Inverse Iteration algorithm for symmetric tridiagonal matrices

We have developed a hybrid procedure based on the Godunov algorithm for computing eigenvectors of tridiagonal symmetric matrices and inverse iteration, which we call the Godunov-Inverse Iteration algorithm. It employs the inverse iteration to improve the accuracy of eigenvectors computed according to the Godunov method with the embedded Modified Gram-Schmidt...

## The wall cells in the cellular automaton of simulation fluid flow

In this paper, the boundary conditions of 2D and 3D Cellular Automaton models (CA models) are considered and classified. It is shown that the simulation algorithm does not change at different boundary conditions, and the computing complexity of simulation is not increased with a large number of wall cells, even...

## Concurrent selection of the shortest paths and distances in directed graphs using vertical processing systems

In this paper, we propose a new implementation of Dijkstra's shortest path algorithm on a model of associative parallel processors with the vertical data processing (the STAR-machine) to obtain for every vertex of a directed graph the distance along with the shortest path from the source vertex. We prove correctness...

## A parallel program for simulation of disc-shaped self-gravitating systems

A model of self-gravitating system is described. Present parallel programs implementation of such a model are reviewed in brief. Numerical algorithm is described. The parallelization technique and load balancing strategy are discussed in detail. The parameters of test computations that meet the requirements of the problem of protoplanetary disc simulation...

## Mapping a parallel program structure onto distributed computer system structure by the Hopfield neural network with fuzzy scheduling parameters

An approach to mapping structure of parallel program onto structure of distributed computer system by the Hopfield neural network is presented. For typical structures of parallel programs ("line", "ring", "mesh", "binary tree") and regular structures of distributed CS ("torus", "hypercube") it is shown that fuzzy control of derivative of neuron...

## The parallelization experience of a multi-program complex. Part 1. The parallelization strategy

Technological aspects of parallelization of the computing system "Potok-3", intended for some numerical modeling of problems of aerodynamics and physical gas dynamics are considered. The methods and problems of global parallelization of a multi-program complex by major parameters, as well as C -, L- and V-types of the parallelization procedures...