To predict emergencies and irreversible consequences of human activities, scientists usemathematical modeling. When an emergency occurs, it is very important to minimize the decisionmakingtime. The development of the project solution can be based on the forecast of changes inthe modeled process. In the numerical solution of problems of hydrophysics and biological kinetics,it becomes necessary to develop effective methods for solving systemic equations of large dimensionwith a non-self-adjoint operator. The large volume of processed information and thecomplexity of computations necessitate the use of computational clusters, which include videoadapters to increase the performance of the computing system and the speed of information processing.The aim of the research is to develop a solution for a module that implements the algorithmof the system of linear algebraic equations (SLAE) by the modified alternative triangulariterative method (MATM) (self-adjoint and non-self-adjoint case) using NVIDIA CUDA technology.A method for decomposition of the computational domain in a three-dimensional case is described.A graph model of a parallel pipeline computational process is proposed, focused on theGPU (Graphics Processing Unit). To determine the two-dimensional configuration of flows in thecomputational unit, when performing one step of one step, the MATM is minimal. The studies haveshown that the choice of the method of decomposition of the computational domain in the form ofparallelepipeds must be performed taking into account the architecture of the video adapter. Thedeveloped algorithm and software module make it possible to more effectively use the computationalresources of the GPU used to solve computationally laborious problems of hydrophysics.

Проценко Софья Владимировна, аспирант кафедры «Математика и информатика», Донской государственный технический университет (Ростов-на-Дону, Российская Федерация) Атаян Ася Михайловна, кафедра «Программное обеспечение вычислительной техники и автоматизированных систем», Донской государственный технический университет (Ростов-на-Дону, Российская Федерация) Чистяков Александр Евгенвевич, д.ф.-м.н., кафедра «Программное обеспечение вычислителвной техники и автоматизированных систем», Донской государственный технический университет (Ростов-на-Дону, Российская Федерация) Никитина Алла Валериевна, д.т.н., доцент, кафедра «Интеллектуальные и многопроцессорные системы», Южный федеральный университет (Таганрог, Российская Федерация) Литвинов Владимир Николаевич, к.т.н., доцент, кафедра «Теплоэнергетика и информационно-управляющие системы», Азово-Черноморский инженерный институт ФГБОУ ВО Донской ГАУ (Зерноград, Российская Федерация) Филина Алёна Александровна, к.т.н., ООО «НИЦ супер-ЭВМ и нейрокомпьютеров» (Таганрог, Российская Федерация) S.V. Protsenko1, A.M. Atayan1, A.E. Chistyakov1, A.V. Nikitina2, V.N. Litvinov3, A.A. Filina4 1 Don State Technical University (Gagarina sq. 1, Rostov-on-Don, 344000 Russia), 2Southern Federal University (Chekhova, 2, Taganrog, 347922 Russia), 3Azov-Black Sea engineering institute of FSBHEEPT “Don State Agrarian University” (Lenina 21, Zernograd, 347740 Russia), 4Scientific Research Center of supercomputers and Neurocomputers (per. Italyansky 106, Taganrog, 347900 Russia) E-mail: rab55555@rambler.ru, atayan24@mail.ru, cheese_05@mail.ru, nikitina.vm@gmail. com, litvinovvn@rambler.ru, j. a.s.s.y@mail.ru

The paper covered the development of solution methods for model of eutrophication of shallow water in view the movement of the water flow, microturbulent diffusion, gravitational settling, spatially uneven distribution of temperature and salinity, and pollutants of nutrients, oxygen, phyto- and zooplankton, etc. Shallow waters of the Azov Sea and Taganrog Bay were selected as the object of simulation. Numerical solution of the problem is based on gradient method of variation type – the method of minimal corrections. The acceleration and efficiency of calculations is achieved with using multiprocessor computer system of Southern Federal University. The solution of the problem of water ecology will allow to predict changes of water quality of shallow reservoirs, and to study the mechanisms of formation of zones with low oxygen content.

В данной статье исследуется федеративное устройство Венесуэлы. Исследуется основной закон Венесуэлы и иная нормативно-правовая база по данной тематике. Рассматривается исторический период становления современной венесуэльской государственности.

The work is devoted to the development of parallel algorithm that takes into account the architecture of supercomputers with shared and distributed memory. A parallel algorithm is developed for the numerical solution of the problem of biological kinetics model of interaction between phyto- and zooplankton. Using the MPI library provides a better distribution of computer resources and increases the effectiveness of the algorithm on distributed computing systems. At the same time for systems with shared memory OpenMP is used, which ensures universality of the algorithm for super-computers with different operating systems.

The work is devoted to the development of methods of solution of the model problem of eutrophication of shallow water body, taking account of the movement of the water flow, microturbulence diffusion of spatially-nonuniform distribution of temperature and salinity in the shallow waters, the Azov sea and Taganrog Bay. Numerical solution of the problem based on the method of minimal amendments. Solution of the problem of eutrophication will allow to predict the quality of the water of shallow water bodies as well as to examine the conditions for the formation of zones with reduced oxygen content in the water (kills phenomens).

The work is devoted to construction of parallel algorithm for shared memory using winapi functions. The algorithm implements the problem of toxic algae Sceletonema costatum spread in a shallow water basin. The problem is urgent as its numerical solution gives calculations of hazardous substances and toxic algae concentration in the sea of Azov. The proposed method of parallel processing implementation allows to reduce run time more than twice. The mechanism of additional threads creating was taken as basis that ensures a better distribution of computer resources and improves the algorithm efficiency.

The developed mathematical model is a combination of high-tech data, which were published in several articles and scientific publications. It considers the movement of the aquatic environment, microturbulence environment motion, salinity, temperature, oxygen conditions and mechanism of outer hormonal stimulation. The solution of the model problem used to diagnose the environmental situation in the Azov Sea and the Taganrog Bay is stable and allows for computational experiments with the verification data in a wide range of control parameters. The results indicate that the use of algae Chlorella Vulgaris BIN for algolization of shallow reservoirs will help to improve the quality of their waters.

Nonlinear spatially-non-uniform 3D-model of interaction of a plankton and food fish population pelengas are derived. The numerical solution of the models are obtained by using the second order accuracy (in space and time), centered, implicit finite difference scheme. The numerical solution is steady; it allows carrying out experiments with a wide range of initial and boundary conditions and values of managing parameters under initial and boundary conditions of a various kind. The estimation, the analysis and forecasting of an ecological condition of shallow reservoirs can be spent by means of the constructed model.