Visualization of the decisions of applied problems in multiprocessor computing systems

Abstract

Abstract. The article is devoted to distributed simulation of visualization of decision vectors of applied problems on the basis of schemes of increased accuracy order. The higher computational speedup in comparison with the finite-difference approach is illustrated by analytical solutions that allow simultaneous and parallel computations in all temporary layers. It is shown that the most promising approach to mathematical simulation of applied problems is the one that is based on numerical-analytical solutions.Keywords: multiprocessor computing system, speedup, visualization, distributed simulation, numerical-analytical solution.Target setting. Significant computation speedup of applied problems is achieved by means of finitedifference schemes due to the parallelization effect. However, the numerical-analytical algorithms for solving applied problems deserve special attention. Greater computational speedup compared to the finite difference approach can be achieved through analytical solutions that allow simultaneous and parallel computing for all temporary layers and, in this case, do not use combined memory. Thus, the most perspective approach to the mathematical simulation of applied problems should be the one that is based on numerical-analytic solutions. Effective means during the processing of heat and mass transfer tasks in metallurgical industry are considered to be the application of parallel computing technologies on distributed cluster-type systems that have relatively low cost and are easily scaled both by the number of processors and by the amount of RAM [2,12]. Consequently, the distributed simulation of the vector visualization of applied problems solutions on the basis of schemes of the raised accuracy order is an essential and relevant task.Analysis of recent research and publications. Heat and mass transfer processes of metallurgical production should be considered as large systems [8][9][10]. Today, solving complex, large-scale tasks requires powerful computers and is characterized by 'parallel' term, that is, there are parallel computers, computing systems, parallel computing methods, etc. [3 − 5]. In broad terms, this term entered almost immediately after the appearance of the first computers, or rather, after realizing the fact that the computers created were not able to solve, during the optimal term, many practical tasks. The emergence in computing systems of new and expensive communication tools, a more advanced elemental base, stimulated the development of high-performance computations based on multiprocessor computing systems [1, 7].In addition, the class of problems in question is usually solved through set of finite-difference equations, which essence is to replace the derivatives by difference relations. In this case, from the numerical algorithm point of view, the solution of finite-difference equations is divided into explicit and implicit schemes [11]. In an explicit scheme, the values of the desired function are determined sequentially, layer by layer. However, despite the appar...

Development of a Linear-Scaling Consensus Mechanism of the Distributed Data Ledger Technology

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