Parallel computational algorithms in thermal processes in metallurgy and mining

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Authors:

G. G. Shvachych, Dr. Sc. (Tech.), Prof., orcid.org/0000-0002-9439-5511, National Metallurgical Academy of Ukraine, Dnipro, Ukraine, e–mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

O. V. Ivaschenko, orcid.org/0000-0003-4394-6907, National Metallurgical Academy of Ukraine, Dnipro, Ukraine, e–mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V. V. Busygin, orcid.org/0000-0003-1130-3616, National Metallurgical Academy of Ukraine, Dnipro, Ukraine, e–mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Ye. Ye. Fedorov, Dr. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0003-3841-7373, Donetsk National Technical University, Pokrovsk, Donetsk region, Ukraine

Abstract:

Purpose. Formation of parallel algorithms in the thermal process simulation in metallurgy and mining. The proposed parallel form of the algorithms must be maximal, and, therefore, have the minimum possible implementation time in parallel computing systems. Elimination of recurrent computation structure of the desired decision vectors, which, as a rule, leads to the rounding errors accumulation. Such class simulation problems are realized by multiprocessor computing systems.

Methodology. Implementation of parallelizing process of mathematical problem definition is realized by an approach based on the “odd-even” reduction algorithm. The essence of this approach lies in exclusion of simulation coefficients of the process under research by realizing elementary rows transformations of the constructed equations system. A directly parallel form of the algorithm for solving problems is realized by a numerical-analytical approach. It is shown that the compiled parallel form is the maximum, which, in turn, provides minimum time for solving the set problems by multiprocessor computing systems.

Findings. The presentedresearch studies in this paper showed a high efficiency of parallelization of systems of tridiagonal structure linear algebraic equations by example of solving thermal problems. The proposed numerical-analytical method for parallelizing tridiagonal systems does not impose any restrictions on the grid nodes topology of the computational domain. With respect to parallel computations of arithmetic expressions, the original data error is separated from the rounding operations by the proposed method. This approach excludes the recurrent structure of the desired decision vectors computation, which, as a rule, leads to accumulation of rounding errors. The proposed parallel form of the algorithms must be maximal, and, therefore, have the minimum possible implementation time in parallel computing systems. Computational experiments conducted by a multiprocessor computer system showed high efficiency of the developed parallel algorithms.

Originality. Within decomposition algorithms, based on the “odd-even” reduction method, a new approach to the distributed solution of linear algebraic equation systems is proposed for the first time, which differs from the known methods in the closed parallel form with respect to the central grid node and with a high degree of vectorization. There was proposed, analyzed and implemented a new approach to the solution of metallurgical production problems, which allows increasing economy, productivity and speed of computations. It is proved that this approach provides the highest computation vectorization degree, predetermines the maximum parallel algorithmic form and, as a consequence, the minimum possible time for implementing algorithms on parallel computing systems.

Practical value. By using a high-performance multiprocessor system, the developed approach allows processing and interpreting the thermal experiments results, and achieving a high accuracy degree, a significant reduction in the processing time of experimental data.

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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