COMPUTATIONAL EXPERIMENTS ON SOLVING GRID ELLIPTIC EQUATIONS BY SOME PARALLEL ITERATIVE METHODS ON THE K60 CLUSTER

The paper deals with the problem of preserving natural water systems, as well as maintaining their integrity, not only through the enterprise of organizational, engineering and technical solutions, but also through the development of highly effective mathematical modeling techniques that make it possible quickly and efficiently, based on interconnected high-precision models of hydrophysics and hydrobiology, predict the processes of pollution spreading and the occurrence of hazardous phenomena in coastal systems. The article considers algorithms for solving grid equations developed for high-performance cluster systems. A model of parallel computations is proposed, which makes it possible, when choosing the appropriate method for solving the problem of aquatic ecology, to estimate the cost of calculations, which is defined as the product of the time of parallel solution of the problem and the number of processors used. An estimate of the optimal amount of information packet for exchange between processors is obtained. The adaptive modified alternating-triangular method of minimum corrections is described, the results of numerical experiments for the parallel variant of this one are presented.