# MODELING OF MAXIMALLY PARALLEL STRUCTURES OF ALGORITHMS FOR SOLVING THERMAL PROBLEMS

## DOI:

https://doi.org/10.34185/1991-7848.2021.01.10## Keywords:

thermal problems, parallel computing, multiprocessor system, parallel algorithm, method of straight lines## Abstract

The paper demonstrates the possibility of creating a maximum parallel form of computational algorithms to solve thermal problems and their mapping to the architecture of multiprocessor systems based on solving thermal problems of mathematical physics. It is shown that an effective tool for studying heat and mass transfer problems in metallurgical production could be parallel computing technologies on distributed cluster systems with a relatively low cost and reasonably easily scalable both in the number of processors and in the amount of RAM. Tridiagonal structure systems' parallelization was implemented by a numerical-analytical approach, which predetermined their maximally parallel algorithmic form. That approach is facilitated by the minimum possible implementation time of the developed algorithm on parallel computing systems. Furthermore, during the arithmetic expressions parallel computations, the developed algorithm separates the error in the output data from rounding operations. Thus, the parallelization of tridiagonal systems based on numerical-analytical discretization methods does not impose any restrictions on the topology of the mesh nodes of the computational domain.

Furthermore, as applied to the parallel computation of arithmetic expressions, it separates the initial data error from a real PC's rounding operations. That approach eliminates the recurrent structure of computing the sought-for decision vectors, which, as a rule, leads to the round-off errors accumulation. Such a parallel form of the constructed algorithm is maximal and has the shortest possible implementation time of the algorithm on parallel computing systems. The developed approach to parallelizing the mathematical model is stable for various types of input data. It has the most parallel form and is distinguished by the minimum time for solving the problem as applied to multiprocessor computing systems. That is explained as follows. If it is hypothesized that one processor can be assigned to one processor and one processor can be assigned to one node of the computational mesh domain, the computations can be processed in parallel and simultaneously for all nodes of the computational mesh domain. The simulation process was implemented on a PC cluster. It follows from the simulation results analysis that the developed method for solving the heat conduction problem effectively minimizes residuals.

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