Organization of parallel-pipeline calculations for modeling the pollutant distribution process in a reservoir

One of the most acute problems for today is the water pollution. For rapid decision in emergency situations, it is necessary to develop effective software and algorithmic tools that allow us to make accurate forecasts of the environmental situation changing of coastal systems. Water pollution of the Azov and Black Seas by storm drains and human waste products leads to an increase of toxic substances concentrations that significantly exceed the maximum permissible values. The pollution transport problem is solved on the basis of the Navier-Stokes and the diffusion-convection-reaction equations. As a result of discretization of the continuous problem of transport of pollutants using the finite-difference approach for a rectangular grid, we obtain a system of linear algebraic equations (SLAE) of large dimension, which require significant time costs. To increase the efficiency of calculations (to reduce the time) on a multiprocessor computer system (MCS), there is a need to develop effective parallel algorithms for solving SLAE. The decomposition method for a two-dimensional computational domain is proposed in this paper, which allows organizing a parallel-pipeline process of calculations as follows: at each stage of calculations, each processor core simultaneously processes fragments of the computational domain that are offset from each other. This process is described in the form of a graph, in which each node corresponds to fragments of the computational domain, and the edges – a sign of the adjacency of fragments.

Parallel algorithms for solving diffusion-convection problems on a multiprocessor computer system using hybrid MPI / OpenMP technology

The paper deals with the mathematical models, algorithms and software for mathematical modeling of coastal systems’ water pollution spreading dynamics under various unfavorable phenomena of natural and artificial genesis, developed for high-performance cluster systems. Methods for partitioning the computational domain for solving diffusion-convection problems have been developed, which allow for efficient parallelization of a computationally complex modeling problem, taking into account the architecture of the multiprocessor system used. The developed mathematical models are based on high-precision models of hydrophysics and hydrobiology and take into account the peculiarities of water systems in the south of the Rostov region, as well as factors of hydrobiological dynamics such as microturbulent diffusion and advective transport in various directions, mechanisms of primary and secondary pollution of coastal systems, taking into account currents. The paper presents algorithms for solving a simulated problem based on MPI parallelization technology, as well as based on mixed MPI + OpenMP technology. Numerical experiments have been carried out and the two technologies efficiency comparison has been made in the conditions of computing cluster used.

The problem of choosing the optimal performance in the multiprocessor computer system design

The article presents the formulation of the problem of optimizing the structure of multiprocessor computing systems designed to solve control problems in real time. The features of this problem, which influence the choice of optimization methods, have been studied. It is concluded that this problem can be effectively solved using evolutionary methods of optimization. The considered models for finding performance can be used to optimize the architecture of multiprocessor computing systems. Besides, it should be taken into account that the resources allocated for the development and operation of computing systems are always limited. Therefore, it is advisable to consider the problem of optimizing the structure of a computing system as multi-criterial one: one criterion is the performance, and the other one is the cost of development and operation of the system. Acquired results can be used in development of multiprocessor computing systems for real-time systems, which is going to reduce the cost of development and operation of these control systems.

SIMULATION OF MICROBIOLOGICAL DESTRUCTION PROCESS OF OIL POLLUTION IN SHALLOW WATER

The paper covers the research of microbiological destruction processes of petroleum origin pollutants in a shallow water taking into account a number of determining factors that affect the distribution of pollution in the researched water area: the oil fractional composition, the processes of evaporation, dissolution, biological oxidation of petro-hydrocarbons by microorganisms, as well as hydrodynamic and chemical-biological features of the water. A complex of interrelated spatially inhomogeneous mathematical models was proposed that allow researching the dynamics of microbiological destruction processes of petroleum hydrocarbons in shallow water. Schemes with weight taking into account the partial filling of computational cells of the simulated domain were developed at model discretization that made it possible to significantly increase the accuracy of calculations and reduce the calculation time. Based on a multiprocessor computer system, experimental software has been developed for predictive modeling of the ecological situation of shallow water in the event of accidental pollution by oil and other harmful substances during natural and technogenic challenges.

The Efficiency of Discrete Optimization Algorithm Portfolios

Introduction. Solving large-scale discrete optimization problems requires the processing of large-scale data in a reasonable time. Efficient solving is only possible by using multiprocessor computer systems. However, it is a daunting challenge to adapt existing optimization algorithms to get all the benefits of these parallel computing systems. The available computational resources are ineffective without efficient and scalable parallel methods. In this connection, the algorithm unions (portfolios and teams) play a crucial role in the parallel processing of discrete optimization problems. The purpose. The purpose of this paper is to research the efficiency of the algorithm portfolios by solving the weighted max-cut problem. The research is carried out in two stages using stochastic local search algorithms. Results. In this paper, we investigate homogeneous and non-homogeneous algorithm portfolios. We developed the homogeneous portfolios of two stochastic local optimization algorithms for the weighted max-cut problem, which has numerous applications. The results confirm the advantages of the proposed methods. Conclusions. Algorithm portfolios could be used to solve well-known discrete optimization problems of unprecedented scale and significantly improve their solving time. Further, we propose using communication between algorithms, namely teams and portfolios of algorithm teams. The algorithms in a team communicate with each other to boost overall performance. It is supposed that algorithm communication allows enhancing the best features of the developed algorithms and would improve the computational times and solution quality. The underlying algorithms should be able to utilize relevant data that is being communicated effectively to achieve any computational benefit from communication. Keywords: Discrete optimization, algorithm portfolios, computational experiment.

Super Fibonacci Graceful Graphs and Fibonacci Cubes

The popularity of Fibonacci cubes is due to their wide range of uses. In mathematical chemistry, this concept is used in the study of hexagonal graphs. In computer science, Fibonacci cubes are interesting from an algorithmic point of view. V. Hsu introduced them in 1993 to simulate the connections of multiprocessor computer networks. He wanted to get graphs with hypercube properties, the order of which is not a power of two. Therefore, the problem of embedding other graphs in Fibonacci cubes is of interest.

Computational aspects of mathematical modeling of the shallow water hydrobiological processes

Статья посвящена изучению нелинейных эффектов в динамике популяции промысловой рыбы пиленгас Азовского моря при низкой и высокой ее численности с учетом эффекта Олли, конкуренции за ресурсы, таксиса, вылова, пространственного распределения биогенных веществ и детрита на основе многовидовой модели взаимодействия планктона и рыб. Дискретный аналог разработанной модельной задачи водной экологии, входящей в состав программного комплекса, получен на основе схем второго порядка точности с учетом частичной заполненности расчетных ячеек. Возникающая в процессе дискретизации система сеточных уравнений большой размерности была решена на основе модифицированного попеременно-треугольного метода, имеющего наибольшую скорость сходимости при условии асимптотической устойчивости разностных схем для параболических уравнений, эффективность которого была улучшена на основе уточненных спектральных оценок. Разработка эффективных параллельных алгоритмов численной реализации поставленной задачи биологической кинетики, ориентированных на многопроцессорную вычислительную систему (МВС) и графический ускоритель NVIDIA Tesla K80 с модификацией формата хранения данных, позволила анализировать процессы воспроизводства популяций биогидроценоза в режиме реального и ускоренного времени. Paper covers the research of nonlinear effects in population dynamics of the pelengas commercial fish of the Azov Sea taking into account the Allee effect, competition for resources, taxis, catching, spatial distribution of biogenic matter and detritus based on a multi-species model of plankton and fish interaction. Discrete analogue of developed model problem of water ecology, included in a software complex, were calculated using schemes of second order of accuracy taking into account the partial filling of computational cells. The system of grid equations of large dimension, arising at discretization, has been solved on the basis of adaptive modified alternately triangual variational method. Effective parallel algorithms were developed for numerical implementation of biological kinetics problem and oriented on multiprocessor computer system and NVIDIA Tesla K80 graphics accelerator with the data storage format modification. Due to it, the reproduction processes of biogeocenose populations have been analyzed in real and accelerated time.