Программирование. Рубрика в журнале - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Model of porous material sintering
Статья научная
The mathematical model of inert porous materials sintering was proposed. As an initial data, the model uses the initial distribution of pore surface elements and time-temperature conditions of sintering. Sintering is modelled by the system of kinetic equations describing shrinkage of a material depending on its initial properties and a time-temperature condition of the process. Experiments on aluminum oxide powder sintering have been carried out in several time-temperature conditions in which linear shrinkage was traced in time. The initial powder particles size distribution was previously measured. A value of main parameters used in the model was determined according to the sample linear shrinkage data measured at the 10 C/min heating rate. Time dependences of linear shrinkage were calculated for the heating rates of 5 and 15 C/min. Comparison of the calculated dependences with experimental data for heating rates 5 and 15 С/min has shown the good qualitative and quantitative concordance.
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Статья научная
In this paper we studied the possibilities of adaptation of Scilab freeware computer mathematic package to the solution of special calculation problems are studied. We modeled and calculated the family of adaptive devices of automation, control and protection for smart/intellectual electric grids including renewable energy sources. We studied the possibilities of Scilab package for sequential calculating using a big number of algebraic functions, solving the systems of linear algebraic equations, analyzing of results, solving the tasks of optimization, building 2D and 3D function diagrams, etc. All calculated solutions obtained from Scilab, were analysed in comparison with the similar solutions calculated in MathCAD. The results confirm the relevance of using the Scilab package for these purposes and demonstrate some of its advantages in education, scientific research and electric engineering calculations.
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Models and methods for three external ballistics inverse problems
Статья научная
We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semi-axis position) when firing an unguided artillery projectile on the assumption that the gun barrel semi-axis can move in a connected nonconvex cone having a non-smooth lateral surface and modelling visibility zone restrictions. In the first problem, the target is in the true horizon plane of the gun, the second and the third problems deal with some region of 3D space. A distinctive feature of the models is that the objective functions are e-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on the algorithm of projecting a point onto e-Lipschitz level function set. A computer programme has been based on it. А series of numerical experiments on each problem has been carried out.
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New approximate method for solving the Stokes problem in a domain with corner singularity
Статья научная
In this paper we introduce the notion of an Rv-generalized solution to the Stokes problem with singularity in a two-dimensional non-convex polygonal domain with one reentrant corner on its boundary in special weight sets. We construct a new approximate solution of the problem produced by weighted finite element method. An iterative process for solving the resulting system of linear algebraic equations with a block preconditioning of its matrix is proposed on the basis of the incomplete Uzawa algorithm and the generalized minimal residual method. Results of numerical experiments have shown that the convergence rate of the approximate Rv-generalized solution to an exact one is independent of the size of the reentrant corner on the boundary of the domain and equals to the first degree of the grid size h in the norm of the weight space W12,v(Ω) for the velocity field components in contrast to the approximate solution produced by classical finite element or finite difference schemes convergence to a generalized one no faster than at an O(hα) rate in the norm of the space W12(Ω) for the velocity field components, where α
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New features of parallel implementation of N-body problems on GPU
Статья научная
This paper focuses on the parallel implementation of a direct N-body method (particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered for models with a number of particles N:105-107. By means of N-body simulations of gravitationally unstable stellar galactic we have investigated the algorithms parallelization efficiency for various Nvidia Tesla graphics processors (K20, K40, K80). Particular attention was paid to the parallel performance of simulations and accuracy of the numerical solution by comparing single and double floating-point precisions (SP and DP). We showed that the double-precision simulations are slower by a factor of 1,7 than the single-precision runs performed on Nvidia Tesla K-Series processors. We also claim that application of the single-precision operations leads to incorrect result in the evolution of the non-axisymmetric gravitating N-body systems. In particular, it leads to significant quantitative and even qualitative distortions in the galactic disk evolution. For instance, after 104 integration time steps for the single-precision numbers the total energy, momentum, and angular momentum of a system with N=220 conserve with accuracy of 10-3, 10-2 and 10-3 respectively, in comparison to the double-precision simulations these values are 10-5, 10-15 and 10-13, respectively. Our estimations evidence in favour of usage of the second-order accuracy schemes with double-precision numbers since it is more efficient than in the fourth-order schemes with single-precision numbers.
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Numerical modelling of the dynamics of the galactic halos in the colliding galaxies
Статья научная
Based on parallel three-dimensional simulation of N-body and gas self-consistent dynamics, we study the behavior of hot coronal gas in the colliding galaxies with "live'' dark matter halos. We model a few scenarios of the galactic collisions including "bull-eye'' and non-central ones, and use different values of the initial velocities of the colliding galaxies. Taking into account the self-gravity, we demonstrate that the collision of gaseous and stellar components does not lead to the formation of a gaseous "protogalaxy'' observed in some numerical simulations. Also, we show that about sixty percent of hot halo gas is expelled into intergalactic space during the collision. Numerical simulations show that a considerable amount of gas (up to 70% for a bull-eye collisions) exchanges between two colliding galaxies.
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Статья научная
The existing mathematical models of pressure swing adsorption (PSA) apply various assumptions regarding the mass and heat transfer mechanisms in the "gas mixture-adsorbent'' system. An increase in the number of assumptions leads to a simplification of the model, a decrease in the calculation time of one iteration in the model and, at the same time, a decrease in its accuracy. The simplification of the model is especially important in PSA processes, since the calculation of the model is carried out before the cyclic steady state and takes tens and even hundreds of cycles (iterations). Ensuring high accuracy of the PSA model and its minimum complexity is a contradictory requirement; therefore it is important to reasonably consider only those transfer mechanisms that are dominant in the model. The paper proposes a mathematical model of the PSA process, which takes into account the thermal effects of sorption, external and internal diffusion mechanisms of adsorptive transfer. A numerical research was carried out to determine the dominant transfer mechanism, and recommendations were proposed for using the preferred PSA model in terms of its accuracy and calculation time (for the processes of air oxygen enrichment and synthesis gas separation). It was found that to calculate PSA oxygen units with a capacity of less than 4 l/min at NTP, it is advisable to use an isothermal model, which saves at least 24,3% of the calculation time with a loss of accuracy of no more than 0,084 vol%. To calculate PSA hydrogen units, the use of an isothermal model is impractical even at the lowest productivity of 50 l/min at NTP. When the diameter of the adsorbent particles is less than 2 mm, it is advisable to use an external diffusion model, which saves at least 54,2% of the calculation time for oxygen units and at least 47,1% of the calculation time for hydrogen units with a slight loss of accuracy. At a gas flow velocity of more than 0,05 m/s, the model can ignore the diffusion in the gas. The research results can be used to calculate various PSA processes for separation of gas mixtures: rPSA, ultra rPSA, VSA, VPSA, and related processes.
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Numerical study of the dynamics of air separation process by pressure swing adsorption
Статья научная
Using mathematical modelling and the finite element method, we carry out the calculation experiments to study the system connections and regularities of pressure swing adsorption process under the conditions of air separation and oxygen concentration (production). We study the influence of mode and construction variables on the dynamics and technological indicators of the effectiveness of this process. Namely, we study the influence of input variables (composition and temperature of atmospheric air, air pressure at the compressor outlet) on output variables (extraction degree, oxygen purity, unit capacity, etc.) of the studied object in a wide range of control variables (adsorption-desorption cycle time, pressure ratios at adsorption and desorption stages, and oxygen-enriched reverse air flow coefficient). Also, we study the influence of construction parameters (layer height, particle diameter and maximum adsorption volume of the adsorbent) on the amount of adsorption, which is equilibrium with the current concentration of the adsorptive in the gas mixture flow on the outer surface of the adsorbent granules, the value of the kinetic adsorption coefficient (the coefficient of external mass transfer of the adsorptive (mainly nitrogen) from the gas phase into the adsorbent). The results of calculation experiments allow to establish the most promising mode and construction parameters for the optimal design of oxygen enrichment systems by pressure swing adsorption with varying pressure.
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On nonparametric modelling of multidimensional noninertial systems with delay
Статья научная
We consider the problem of noninertial objects identification under nonparametric uncertainty when a priori information about the parametric structure of the object is not available. In many applications there is a situation, when measurements of various output variables are made through significant period of time and it can substantially exceed the time constant of the object. In this context, we must consider the object as the noninertial with delay. In fact, there are two basic approaches to solve problems of identification: one of them is identification in «narrow» sense or parametric identification. However, it is natural to apply the local approximation methods when we do not have enough a priori information to select the parameter structure. These methods deal with qualitative properties of the object. If the source data of the object is sufficiently representative, the nonparametric identification gives a satisfactory result but if there are «sparsity» or «gaps» in the space of input and output variables the quality of nonparametric models is significantly reduced. This article is devoted to the method of filling or generation of training samples based on current available information. This can significantly improve the accuracy of identification of nonparametric models of noninertial systems with delay. Conducted computing experiments have confirmed that the quality of nonparametric models of noninertial systems can be significantly improved as a result of original sample «repair». At the same time it helps to increase the accuracy of the model at the border areas of the process input-output variables definition.
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Статья научная
We consider the problem of scheduling cargo transportation on a railway network segment. The railway network is represented by an undirected multigraph. The traffic along the edges of the multigraph is carried out only at certain intervals - using "subthreads". We formulate a new mathematical model of traffic along the edges of the multigraph. A universal criterion of optimality for the scheduling problem is proposed. We propose an algorithm to find a suboptimal solution. A meaningful example is given.
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Optimization of nozzle layout in continuous casting machine
Статья научная
The article presents the results of the scientific research around development of mathamatical foundation for calculating optimal nozzle layout in secondary cooling zone of continuous casting machine and describes implementation of this foundation in specialized computer-aided design system. Optimization procedure is based on the 2-dimensional mathematical model of the thermal state of the slab, which accounts nozzle layout, and optimization criteria for the cross-cut thermal profile of the slab surface. Optimization problem solution consists of two basic blocks: solving thermal conductivity problem and iterative search of the nozzle positions that provide best solution from the point of proposed criteria. The results of running optimization procedure on input conditions based on existing casting machine showed that the obtained solution enables to provide smoother cross-surface thermal profile of the slab. Results of the work can be used for design of new continouous casting machines, modernization of the secondary cooling system of existing machines, and general numeric analisys of secondary cooling system operation for user-provided conditions.
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Статья научная
One of the most interesting and relevant approaches for solving optimization problems are parallel algorithms that work simultaneously with a large number of tasks. The paper presents a new parallel algorithm for NACO that is a hybrid algorithm that consists of the Ant Colony Optimization method combined with the Neighbour Joining method to get accurate and efficient results when solving the Traveling Salesman Problem. Through carrying out comprehensive experiments using a wide variety of real dataset sizes and the multi-core system, the practical results show that the developed program outperforms NACO in terms of execution time and consumed storage space. Availability and implementation: source codes in MATLAB 2017 are publicly available at Internet[i].
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Статья научная
For the analysis of huge problems which are very sensitive to the rounding errors, the software providing rational calculations is developed. Software uses MPI interface for communication in the distributed computational environment. Improved efficiency of such software my be achieved by using heterogeneous computation systems. Local arithmetic operations with long numbers may be done in parallel mode with a lot of processes per one operation. This work introduces the research of increasing of the scalability of basic arithmetic operations.Abilities of the massive parallelism for the heterogeneous computation systems for the efficiency improving are shown. Redundant numerical system with a constant time of the addition operation is introduced. It allows to design well scaled algorithms for all basic arithmetic operations with integer numbers. Scalability of the basic integer arithmetic algorithms is easy applied to rational arithmetic.
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Parametric identification based on the adaptive unscented Kalman filter
Статья научная
The detailed adaptive unscented Kalman filter algorithm is provided. Step-by-step schemes of filtering algorithms used for the software development are given. Nonlinear filtering algorithm efficiency is investigated with considering an example of a nonlinear continuous-discrete model. The statistic estimator based on the continuous-discrete adaptive unscented Kalman filter with noise is proposed for the nonlinear system parameters estimation. The solution to the problem of solar radiation parameters estimation based on the maximum likelihood method and the adaptive unscented Kalman filter is shown. The obtained results lead to significant improvement of satellite trajectory prediction quality.
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Статья научная
Prediction of a new object state at a lack of the known characteristics and estimates of quality indicators of a number of studied objects (a set of reference data) often leads to the problem of multicollinearity of basic data. We propose the following three ways to overcome this problem relating to the sphere of data mining: use a ridge regression, train with the teacher a two-layer neural network, consecutive adapt a single-layer neural network. Also, we compare characteristics of the proposed ways. In the ridge regression method, the introduction of a regularizing term into the LMS equation gives an approximate solution with a sufficient degree of accuracy. A disadvantage of use of the two-layer neural network "feed-forward backprop" and the procedure of training with the teacher "train" is that adjusted weights of the neural network take chaotic (and even negative) values that contradicts a common practice of examination. The following features are revealed: considerable dispersion of weights and shifts of a neural network, ambiguity of the solution due to the choice of random initial conditions, strong dependence on a training algorithm. In order to overcome this shortcoming, we propose a transition to consecutive adaptation of a single-layer neural network with fixing shifts of neurons at zero level.
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Recovering of the heat transfer coefficient from the temperature measurements
Статья научная
An inverse analysis is used to recover the heat transfer coefficient in heat conduction problems from boundary measurement of the temperature. The numerical scheme is based on the finite element method in the space variables, the method of finite differences in time, and a special iteration scheme to determine the heat transfer coefficients on each time step. The heat transfer coefficients is sought in the form of a finite segment of a series with unknown Fourier coefficients depending on time. The algorithm for solving the problem relies on theoretical results stating that this problem is well-posed and can be reduced to an operator equation with a contraction. The results of numerical experiments confirm theoretical arguments that this problem is indeed well-posed. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm. It is stable under random perturbations of the data.
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Статья научная
We propose an approach to simulation of information protection processes at informatization objects in the dynamics of realizing threats of its leakage through technical channels using the apparatus of composite Petri–Markov nets. We investigate the interrelationships of the processes of transferring information at the object of informatization, its interception by a violator from outside this object through technical channels and protection against interception. Analytical expressions are obtained for calculating the probabilistic-temporal characteristics of simulated processes in order to assess the possibility of a violator implementing threats of information leakage at objects of informatization; protection of this information through the use of preventive measures aimed at blocking or anticipating the actions of the violator to implement these threats
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Статья научная
It is shown that multistage concurrent games, or relay-races, are widely used in practice. It is proposed to model relay-races in the state space, in which discrete co-ordinates are the mathematical analogue of stages, which participants pass in the current time, and basic principle of modelling of residence of participant in space states is the M-parallel semi-Markov process. With use of the proposed formalisms formulae for evaluation of stochastic and time characteristics of relay-races evolution are obtained. For arbitrary realization of switching trajectory the recurrent procedure of evolution with evaluation of stochastic and time characteristics of realization under investigation is worked out. Conception of distributed forfeit, which depends on difference of stages of participants compete in pairs is introduced. Dependence for evaluation of total forfeit for every participant is obtained.
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SkifCh: эффективный коммуникационный интерфейс
Статья научная
В работе описывается SkifCh - низкоуровневый интерфейс передачи сообщений. Данный интерфейс эффективно поддерживается на уровне сетевого оборудования, которое, в свою очередь, может быть реализовано в ПЛИС (как сделано в суперкомпьютере СКИФ-Аврора) или в специализированных микросхемах. Интерфейс SkifCh может быть использован для высокоэффективных сетевых обменов непосредственно из прикладных программ, а также для реализации коммуникационных библиотек более высокого уровня. На данный момент поверх интерфейса SkifCh реализованы системы MPI, SHMEM, GASNet и ARMCI. В работе также приведено сравнение эффективности использования SkifCh и MPI на суперкомпьютере СКИФ-Аврора.
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Software set of intellectual support and security of LMS MAI Class.Net
Статья научная
The article discusses integration of mathematical methods and security components in a learning management system (LMS). The discussed methods provide a statistical analysis of user data in process of online training in mathematical disciplines and adapting the content of the system for different users. The software package allows automatic calculation of questions complexity and user ratings by using statistical data. This helps the system administrator to detect users which use illegal hints or help from others. A procedure is designed for content selection for a variety of tests and control activities, with restrictions and without a time limit for the test. Two probabilistic models were used during development of mathematical methods: the Rasch model to describe the probability of users' answer correctness and Van der Linden model to describe the time it took for a user to respond to the question. The software package contains special optimization procedures that estimate the parameters of these models based on the accumulated statistics across all users. Apart from discussing efficiency of LMS usage with the above mentioned methods, the article also discusses general security architecture of the LMS, a set of technologies used for developing system security with specific implementation examples.
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