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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2012  EXPLICIT, FULLCONSERVATIVE VARIATIONAL DIFFERENCE SCHEME FOR GAS DYNAMIC EQUATIONS IN LAGRANGIAN VARIABLES
A. M. Stenin VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 316.
An explicit conservative difference scheme providing the calculation of all grid quantities at one and the same time with integral indexes has been developed using the fully discrete (in space and time) variational method. 3D flows are considered for definiteness. Key words: fully discrete variational method, conservative scheme, crosstype scheme, 3D gas dynamics, volume of a hexahedral cell.
 INTEGRATING THE NUCLEAR COMPOSITION EVOLUTION EQUATIONS OF MATERIALS IN STATIC RADIATION FIELDS D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 1728.
It is impossible to use precision methods for some problems. This is true, in particular, for nonlinear problems associated with finding the parameters of material exposed to radiation. Though approximations, which consist in dividing a time interval into sections of a constant radiation density, are permitted for such problems, the resultant set of linearized problems also has no exact solution, in general case.To find approximate solutions to such problems, a set of schemes of different orders of accuracy based on representing a linear operator as a sum of two operators is proposed. One of them has a high norm, however, it admits an exact solution. The second one having a low norm is considered to be a small addin. With such approach it is possible to estimate the obtained solution accuracy, or estimate the numerical integration step required to provide the given accuracy. The correspondence of the estimated accuracy and error is considered by the example of methodological problems. Key words: nuclear composition, isotope composition, reactor, burnup, decay, reaction crosssection, Cauchy problem, numerical methods, integration scheme, order of accuracy, estimation of errors.
 AN ALGORITHM OF ATOMICSCALE DETECTING A VACANCY PORE AND DESCRIBING ITS SHAPE A. I. Kul'mentiev VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 2942.
An algorithm is proposed that allows detecting packaged clusters of atoms with perturbed crystallinity, identifying the cluster boundary and shape, and measuring its volumetosize ratio during the successive multilevel simulation process. The computer experiment we have performed simulates the spherical pore collapse. The pore shape parameter dependences on the volumetosize ratio have been obtained and compared with the existing analytical expressions. Key words: computer simulation, reactor material science, spaceandtime scales, vacancy pores.
 SIMULATION OF HIGHSPEED SPALL IMPACTS ON MULTIPLELAYER BARRIERS USING THE CLUSTER DYNAMICS METHOD B. L. Voronin, M. V. Zdorova, S. V. Kopkin, M. V. Vetchinnikov, I. A. Davydov, E. A. Pronin VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 4351.
Many engineering problems require the knowledge of the resistances of some structures to impact and penetration. Currently, we have a limited ability of experimentally simulating highspeed impacts (impacts at a speed of sim 47 km/s), first, because of high costs of such simulations and, second, because of a small amount of recorded data that does not allow tracking the dynamics of the whole process in the system of interest. In view of the reasons above and capabilities of the modern computing systems, it becomes clear that numerical simulations are very useful for studying the impact problems in more details. Results of simulations may provide the profound understanding of strains in structures. The RFNCVNIIEF Department of Mathematics has been studying the problem of highspeed penetration of barriers by projectiles beginning from the 1990's. Various mathematical techniques were used for 2D and 3D simulations of the model (or similar) experiments. The paper presents MoDyS code for solving with the cluster dynamics method the problem of a steel ball impacting on a multiplelayer barrier at a highspeed. Results of simulations using the method and comparison with the available results of experiments and simulations by other codes are presented. Key words: MoDyS, cluster dynamics, breaking through barriers, MieGrueneisen potential, monocrystal, polycrystal, arithmetic accelerators.
 CODE COMPLEX FOR MONTECARLO SIMULATIONS OF CRITICAL PARAMETERS ON HYBRIDARCHITECTURE COMPUTING SYSTEMS A. S. Rybkin, A. N. Zalyalov, A. G. Mal'kin, S. P. Ognev, V. I. Roslov, I. V. Semenov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 5258.
The paper presents results of the development of SMKU code that ports the major part of a code calculating the critical parameters of SMK code system to graphical arithmetic accelerators. Benchmarks typical for a given problem class and our first numerical experiments with the developed code on hybridarchitecture computers are presented. The results obtained using arithmetic accelerators NVIDIA demonstrate, for example, sim 16 times gain in speed in simulations for a set of fuel assemblies in comparison with simulations on a onecore generalpurpose Intel processor with Nehalem architecture and sim 13 times gain in speed in Kfactor simulations for the WWER1000 reactor core. Key words: arithmetic accelerator, graphic processor, specialpurpose desktop supercomputer, WWER1000, fuel element, fuel assembly.
 CODE COMPLEX FOR THE MD SIMULATION ON HYBRIDARCHITECTURE COMPUTERS I. A. Kryuchkov, S. V. Kopkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 5965.
MD code complex is used for the molecular dynamics simulation of processes determining the properties of structural materials. In our previous efforts we achieved certain results on the adaptation of various parts of this complex to hybridarchitecture computers. The current paper describes some new capabilities that allow taking into account interactions between particles of both the same and different types. We tested the main types of particle interactions in a single accelerated version of MD complex of codes to study a possibility of using different hybrid computers, in particular, a multiprocessor and a specialpurpose desktop hybrid computing system GVS10 "Kuban".The MD code complex runtimes on graphical and generalpurpose processors, as well as on graphical processors of different types were compared for the main types of problems.The obtained results demonstrate that arithmetic accelerators can be used efficiently for the MD problems. Key words: graphical arithmetic accelerator, processor, code, performance, molecular dynamics, potential.
 PRACTICAL IMPLEMENTATION OF RECOGNIZING A BODY IMAGE USING NEURAL NETWORK A. A. Fertsev VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 1. P. 6675.
The paper describes the implementation of a neural network, which is trained using an algorithm based on the LevenbergMarquardt algorithm. NVIDIA CUDA technology provides a 16 times higher rate of training the developed neural network. The neural network is used for recognizing noisy images. Key words: image recognizing, neural network, LevenbergMarquardt algorithm, GPU, CUDA.
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