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.