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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2021  AN ALGORITHM OF SOLVING LINEAR DIFFERENCE EQUATION SYSTEMS ON REFINED GRID CELLS
A. M. Stenin VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 316.
The paper presents an algorithm of solving linear difference equation systems on adaptively refined grid cells, which is based on the method used to solve linear algebraic equation systems on graphs and allows paralleling computations. The algorithm of the method is described as applied to the difference splitting scheme for solving the 3D heat conduction equation, however, it can be used to solve equations describing some other physical processes on refined spatial grids, as well. Key words: threedimensional heat conduction, difference splitting schemes, refined grids, linear difference equations on graphs, paralleling of the sweep.
 THE IMPACT OF THE SPECTRAL RADIATION TRANSPORT EFFECTS IN DIFFERENT APPROXIMATIONS ON THE DEVELOPMENT OF SHORTWAVELENGTH PERTURBATIONS IN THE INERTIAL CONFINEMENT FUSION TARGETS V. A. Lykov, E. L. Lyagina, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 1728.
Using a 2D radiation hydrodynamics code, the impact of spectral radiation transport effects in different approximations on the development of shortwavelength perturbations in shell targets for the inertial confinement fusion is investigated. It is shown that the shell motion dynamics and perturbation growth rate during the target compression significantly depend on the radiation transport model. The impact of the Mband of the hohlraum Xrays on the target heatup and development of shortwavelength perturbations under the publiclydisclosed conditions of NIF experiments with indirectdrive targets is considered. It is observed that the shell heating up by gammas from Au ion Mtransitions decreases the shell density, as well as the density and pressure gradients, and leads to a weaker growth of perturbations. Results of 2D simulations of the perturbation growth with the spherical harmonic numbers 60 and 90 in multigroup radiation transport approximations are in a good agreement with data obtained in the NIF experiments with shell targets. Key words: Xrays transport, the inertial confinement fusion problem.
 THE EXACT SOLUTION TO ONE MODEL PROBLEM OF ELECTROMAGNETIC FIELDS GENERATED BY A POINT SOURCE OF GAMMAS A. A. Solovyev VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 2938.
The problem of electromagnetic fields generated by outside volume currents simulating currents of Compton electrons due to the scattering of gammas from a point source in a homogeneous nonconducting atmosphere is considered. These currents are prescribed to be factorized with the specified angular and time dependences, while the dependence on the distance to the source may be practically arbitrary. The exact solution was found in the form of singlefold quadratures for each of the three electric field components. It can be used as a representative benchmark to verify the numerical techniques for nonstationary electromagnetic fields. Key words: Maxwell´s equations, volume currents, Compton electrons, a homogeneous nonconducting medium, benchmarks for numerical techniques.
 IMPLEMENTATION OF A METHOD FOR SOLVING THE 2D HEAT CONDUCTION EQUATION ON THE HYBRID ARCHITECTURE (CPU + GPU) V. O. Anisov, E. V. Vaziev, D. A. Ushakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 3952.
The paper presents a way of organizing the computation process on a hybridarchitecture computer: a generalpurpose processor (CPU) and a graphics accelerator (GPU). A numerical method for solving the 2D heat conduction equation was implemented on the architecture with twolevel parallelism. An unstructured grid of arbitrarily shaped triangular and quadrangular cells was used. The heat conduction equation solution is reduced to solving a system of linear equations using the conjugate gradient method. The paper analyses the iterative part of the method. Paralleling on a distributed memory is performed by decomposing the original grid into subdomains, with each subdomain being calculated using its own MPI process either on CPU (MPI+OpenMP), or on GPU (MPI+CUDA). The authors mean that the hybrid compute process is the concurrent use of the both options. A simple formula has been obtained to find decomposition parameters, which allows achieving a maximum hybrid computing performance. This formula is based on the assessment of the memory subsystem capabilities for the devices in use, because the memory bandwidth is the major speedlimiting factor for the method presented. In simulation experiments on one node, the hybrid compute mode efficiency was 7589%. Key words: hybrid computing, heat conduction, conjugate gradient method.
 COMPUTATION PARALLELING METHODS IN THE "RADUGA T" CODE TO SOLVE THE NEUTRON TRANSPORT EQUATION ON UNSTRUCTURED GRIDS O. V. Nikolaeva VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 5367.
The problem of paralleling computations when solving the integrodifferential transport equation using unstructured grids is considered. Paralleling is performed by fragmenting a spatial grid into subdomains, with computations being carried out on its own MPIprocess for each subdomain. Two computation paralleling methods implemented in the "Raduga T" code are discussed: the BJ (BlockJacobi) and BS (BlockSeidel) methods. In the BJ method simple iterations with respect to the collision integral and values obtained at the boundaries of spatial domains are performed. In the BS method, which follows the idea of the wellknown KBA (KochBakerAlcouffe) method, simple iterations are performed with respect to the collision integral alone. Hence, the BS method has a less number of simple iterations, than the BJ method, however, a longer time is spent to perform them. There has been examined the efficiency of the BJ and BS methods of paralleling computations in the solution of a model problem using the "Raduga T" code. Key words: the neutron transport equation, unstructured grids, parallel algorithms, the BlockJacobi method, the BlockSeidel method, the KBA method.
 SOLVER ADAPTATION TO A SLAE FLUX V. A. Erzunov, Yu. G. Bartenev VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 6879.
At RFNCVNIIEF, a number of codes for the computational physics problems use the PMLP/ParSol library for iteratively solving linear systems of algebraic equations with sparse matrices, both in serial and parallel compute modes. SLAEs are solved on the distributedmemory (message passing interface, MPI) and sharedmemory (OpenMP interface) platforms by calling for an appropriate solver with the given preconditioner. To reduce the SLAE solution time, it is useful to have a capability of changing over from one solver to another during the compute process that allows the user not to perform initial selection of an optimum solver for the problem and replace it by another solver, which is most appropriate for the SLAE properties changed within the problem runtime. This means it is necessary to have an adaptive mechanism for automatically selecting solvers for the problem and the particular stage of simulating the physical process. The adaptive mechanism parameters are set in the PMLP/ParSol library file, where the methods tested and their parameters are specified for the optimum SLAE solution process. After the SLAE solution using one method has been examined, the adaptive mechanism allows testing another method and continues computations using the most optimum one of all the tested methods. The adaptive mechanism of selecting a solver has been verified on nonlinear and linear heat conduction problems using various RFNCVNIIEF codes. Computations demonstrate that the adaptive mechanism reduces the SLAE solution time and the entire problem runtime. Key words: system of linear algebraic equations (SLAE), sparse matrices, distributedmemory computing systems, multicore sharedmemory processors, adaptive mechanism.
 PROBLEMS IN TOOL DEVELOPMENT FOR PROGRAMMING THE AGENT BEHAVIOR LOGIC IN MULTIAGENT SYSTEMS FOR THE SIMULATION OF TWOSIDE MILITARY OPERATIONS K. V. Ivanov, M. V. Galkin, A. I. Sayfullin, R. N. Sayfullina, D. V. Devyatykh VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 1. P. 8090.
The paper considers the key aspects of developing tools for programming the agent behavior logic in multiagent systems and discusses the tool development problems. A brief review of existing agent logic programming tools, including both foreign and domestic software products, is given. The paper is focused on the simulation of twoside military operations for experts in this subject area. For the simulation purposes, three types of agents are identified: a tactical unit, a tactical group, and a command (large unit). The structure of their communication and interactions and specific features of each agent type are described. For each agent type, a solution is proposed to identify the most appropriate tool for programming the agent behavior logic, which is easy to use by experts in the subject area. Key words: simulation, an agent, a multiagent system, programming, behavior logic, management system.
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