PARALLEL IMPLEMENTATION OF THE YANENKO METHOD FOR SOLVING THE HEAT EQUATION

Abstract

In this article, we will consider the parallel implementation of the Yanenko algorithm for the two-dimensional heat equation, and the sweep method was used to numerically solve  the heat equation. The implementation of the sequential  program is carried out simply in two-part steps by the longitudinal-transverse run, however, parallelization of two fractional  steps with an indefinite scheme is difficult due to the creation of inter-process communication of data. In the course of the study, a parallel data distribution with one-dimensional decompositions is shown in the application of the Yanenko method for calculating heat conductivity. The results of parallelization of this task using the 1D decomposition were obtained and acceleration and efficiency images were analyzed in order to evaluate the parallel program. Currently, modeling of processes by numerical solution of differential equations is widely used in every field of Science, the most common methods bring the differential problem to a system of linear algebraic equations, methods that solve such systems include various startup options. The emergence and development of computing systems using Multi-Core processors and graphics accelerators make the problem of startup parallelization relevant; the results of the study are used for teaching in research institutes and universities.