A software package for solving grid equations in areas with geometry "stretched" along one of the spatial directions

Abstract

A method for solving grid equations in areas with geometry "stretched" along one of the spatial directions is proposed. Method proposed for model includes pollutants whose concentration in the Azov Sea, according to the analysis of scientific publications and environmental databases, exceeds the maximum permissible concentration (MPC). The mechanism of the preconditioner formation is described. The estimation of the minimum and maximum eigenvalues is performed. Using object-oriented analysis and design, a class library has been implemented to solve the problem of impurity propagation in a shallow reservoir. The architecture of an information system to support scientific research capable of functioning in conditions of using heterogeneous computing environments is described. The system is based on the requirement of the maximum possible use of free software in order to minimize capital and operational costs. The system uses classes that allow you to read and write information about the geometry of the object under study and the parameters of the calculated grid. Numerical experiments were carried out using the developed software package, including the proposed mathematical model, focused on the multiprocessor computing system (MCS). The dependences of the SLAE solution time on the number of diagonals and the order of the matrix are obtained. The number of iterations for solving grid equations has been experimentally determined depending on the ratio of the number of nodes in spatial coordinates.