Програмно-алгоритмічне забезпечення паралельного розрахунку неізотермічного вологоперенесення на підставі апарату похідних дробового порядку

Abstract

A new mathematical model of the nonstationary process of heat and moisture transfer in the two-dimensional region is constructed on the basis of the use of Caputo and Grunwald- Letnikov derivatives. An implicit finite-difference scheme for approximation of a mathematical model of noisothermal moisture transfer taking into account the fractional integro-differential apparatus is developed. The given algorithm of numerical realization of model allows to receive values of function of temperature and humidity for all points of area of partition. The method of fractional steps is adapted for numerical realization of mathematical model. It allowed performing parallel calculations of two difference half-step taking into account the corresponding spatial coordinate. The implemented algorithm of parallel calculation of non- isothermal moisture transfer in materials of fractal structure makes it possible to obtain a reliable result without the need to conduct complex and expensive practical experiments. It is proposed to use the Model-View-Presenter design pattern for software development. The software a parallel algorithm using .Net threads and algorithmic features of the TPL library has developed. It has been tested on multi-core computer systems with CPUs of different capacities. The .NET Stopwatch class was used to measure the execution time of sequential and parallel algorithms. A two-dimensional case with a mesh partition is studied for three cases: a square shape, a wide rectangular shape, and a tall rectangular shape. Graphs of dynamics of acceleration and efficiency of algorithms are given, and their analysis is also carried out. To smooth the graphs of acceleration and efficiency of algorithms, we apply approximation of experimental data based on the obtained results.