Model of a Parallel-Pipeline Computational Process for Solving a System of Grid Equations

Abstract

Introduction. Environmental problems arising in shallow waters and caused by both natural and man-made factors annually do significant damage to aquatic systems and coastal territories. It is possible to identify these problems in a timely manner, as well as ways to eliminate them, using modern computing systems. But earlier studies have shown that the resources of computing systems using only a central processor are not enough to solve large scientific problems, in particular, to predict major environmental accidents, assess the damage caused by them, and determine the possibilities of their elimination. For these purposes, it is proposed to use models of the computing system and decomposition of the computational domain to develop an algorithm for parallel-pipeline calculations. The research objective was to create a model of a parallel-conveyor computational process for solving a system of grid equations by a modified alternating-triangular iterative method using the decomposition of a three-dimensional uniform computational grid that takes into account technical characteristics of the equipment used for calculations.Materials and Methods. Mathematical models of the computer system and computational grid were developed. The decomposition model of the computational domain was made taking into account the characteristics of a heterogeneous system. A parallel-pipeline method for solving a system of grid equations by a modified alternating-triangular iterative method was proposed.Results. A program was written in the CUDA C language that implemented a parallel-pipeline method for solving a system of grid equations by a modified alternating-triangular iterative method. The experiments performed showed that with an increase in the number of threads, the computation time decreased, and when decomposing the computational grid, it was rational to split into fragments along coordinate z by a value not exceeding 10. The results of the experiments proved the efficiency of the developed parallel-pipeline method.Discussion and Conclusion. As a result of the research, a model of a parallel-pipeline computing process was developed using the example of one of the most time-consuming stages of solving a system of grid equations by a modified alternating-triangular iterative method. Its construction was based on decomposition models of a three-dimensional uniform computational grid, which took into account the technical characteristics of the equipment used in the calculations. This program can provide you for the acceleration of the calculation process and even loading of program flows in time. The conducted numerical experiments validated the mathematical model of decomposition of the computational domain.

Keywords

• parallel algorithm
• computational process
• grid equations