NUMERICAL IMPLEMENTATION OF A PARALLEL ALGORITHM FOR SOLVING THE PROBLEM OF POLLUTANT TRANSPORT IN A RESERVOIR ON A HIGH-PERFORMANCE COMPUTER SYSTEM

Abstract

The purpose of this work is to create a software package for a distributed solution of the problem of transporting a pollutant in a reservoir with complex bathymetry and the presence of technological structures. An algorithm has been developed for the parallel solution of the problem of transporting a pollutant (pollutant) in a reservoir on a graphics accelerator controlled by the CUDA (Compute Unified Device Architecture) system; a comparative analysis of the operation of algorithms on a CPU (Central Processing Unit) and on a graphics accelerator GPU (Graphics Processing Unit) made it possible to evaluate their performance. The software implementation of the modules included in the complex is described, the main classes and implemented methods are documented. The results of numerical experiments showed that solving of pollutant transport’s problem based on the CUDA technology is ineffective for small grids (up to 100 ´ 100 computational nodes). In the case of large grids (1000 ´ 1000 computational nodes), the use of CUDA technology reduces the computation time by an order of magnitude. An analysis of the experiments carried out with the developed components of software showed that the maximum value of the ratio of the algorithm operating time that implements the set task of transferring matter in a shallow water on a GPU to the operating time of a similar algorithm on the CPU was 24.92 times, which is achieved on a grid of 1000 ´ 1000 computational nodes. Implementation of methods for decomposition of grid regions is proposed for solving computationally laborious problems of diffusion-convection, including the problem of transporting pollutants in a reservoir with complex bathymetry with technological objects that take into account the architecture and parameters of a MSC (Multiprocessor Computing System) located on the basis of the infrastructure facility of the STU (Scientific and Technological University) “Sirius” (Sochi, Russia). Consideration was made for such a property of a computing system as the time it takes to transmit and receive floating point data. An algorithm for the parallel solution of the task under the control of MPI (Message Passing Interface) technology has been developed, and its efficiency has been assessed. The acceleration values of the proposed algorithm are obtained depending on the number of involved computers (processors) and the size of the computational grid. The maximum number of computers used is 24, the maximum size of the computational grid was 10 000 ´ 10 000 computational nodes. The developed algorithm showed low efficiency for small computational grids (up to 100 ´ 100 computational nodes). In the case of large computational grids ( from 1000  1000 computational nodes), the use of MPI reduces the computation time by several times.