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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2002  PARALLEL COMPUTATION TECHNOLOGIES FOR RADIATIVE TRANSPORT PROBLEM
E.F. Lelikova, L.I. Rubina, O.N. Ul'yanov, M.A. Chashchin VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 313.
A radiative transport problem is considered in a plane layer. Quantitative properties of the functions, representing solutions of relevant mathematical problems are discussed and studied. Two algorithms (MAPI and MPLCh) are proposed for numerical simulation of radiative transport in a heterogeneous plane layer of finite thickness with a multicomponent mixture. For the algorithms (MAPI and MPLCh) parallel codes and algorithms have been developed and studied in MPI and DVM parallel programming models. A technique was developed to solve informal problems on radiative transport in a reasonable time using multiprocessor computation systems.
 A CRASHPROOF TECHNIQUE FOR COMPUTING FLOWS IN CONTINUUM USING LAGAK TECHNIQUE ON MULTIPROCESSORS S.M. Bakhrakh, S.V. Velichko, V.F. Spiridonov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 1421.
Fundamentals of LAGAK technique for computing unstable flows of multicomponent continuum, principles of its implementation in the complex of the same name, principles of the codes parallelization and basics of approach to the development of a crashproof computation technique are presented. The examples of computations are given.
 3DIMENSIONAL SIMULATION OF DIRECT AND INVERSE RAYLEIGHBENAR AND RAYLEIGHTAYLOR PROBLEMS A.I. Korotky, I.A. Tsepelev VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 2232.
The paper describes one of the possible approaches to numerical simulation of direct and inverse (retrospective) problems of 3D motions dynamics for highly viscous nonuniform incompressible fluid both with regard of heat transfer into fluid and without it. Mathematical model for fluid dynamics includes a quasistationary Stokes equation, a heat balance equation and some equations of physical medium parameter transfer. Many applications of the model for fluid and its motions belong to the geophysics field, though other applications are by far possible. The problems are computed using method with time iterations. For computing rate field of fluid twocomponent vector potential is used, which is obtained by finite element method with special basis composed of threecubic splines. Temperature field in direct time is calculated by difference method using a chart of longitudinaltransversal run. In reverse time the equation of heat balance is solved by variational method, consisting in both the construction of sequential approximations and the solution of a series of specially designed direct problems. Transfer equations are alculated by characteristic method with subsequent interpolation of calculated values using threelinear splines. The results of specific examples calculations are demonstrated.
 GENERATION OF OPTIMAL GRIDS IN MULTIPLY CONNECTED DOMAINS WITH COMPLEX TOPOLOGIES ON MULTIPROCESSOR COMPUTERS A.F. Khairullin, O.B. Khairullina VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 3339.
The survey of works on automatic generation of optimal multiblock curvilinear grids of big size (about hundreds of millions of nodes) in twodimensional domains of arbitrary connectivity and configuration for minimal data has been done. The comparison of sequentional and parallel algorithms has been carried out.
 PARALLEL COMPUTATION VISUALIZATION TASKS V. L. Averbukh, A. Yu. Baydalin, P. A. Vasev, D.R. Ismagilov, A. I. Zenkov, D. V. Manakov, D. S. Perevalov, M. R. Shagubakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 4052.
In the paper the main problems of parallel computation visualization are described. The examples of Western visualization systems are analyzed. The Scientific Visualization and Software Visualization systems developed in the Institute of Mathematics and Mechanics, the Ural Branch of the Russian Academy of Sciences are considered.
 NUMERICAL ALGORITHM FOR SOLVING 3D EQUATIONS OF MICROPULSATIONS THROUGH IONOSPHERE K.G. Gaynulin, V.A. Zhmaylo, Yu.F. Kir'yanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 5359.
For a wide range of issues on ionospherical plasma dynamics, such as the affects associated with generation and micropulsations transmission with regard to effect of geomagnetic field, equations of plasma dynamics are used. The key part in the analysis of perturbations transmission in plasma is played by Maxwell equations for electromagnetic field, an equation of quasineutral ionospherical plasma dynamics and Ohm's law analog. The paper gives a system of micropulsation transmission equations and numerical algorithm for its solution in a 3D square coordinate system. When numerically solved a complex nonlinear system of equations is reduced to the equation of the second order in time variable for the electric field strength by elimination of the magnetic field strength vectors, a current density with the conduction and a speed of the plasma motion. A numerical scheme has been designed on the basis of a longitudinaltransversal directions method similar to a wellknown Duglas scheme for approximating the obtained 3D equation system relatively vector projections. The scheme is implicit in each space variable with the weight factor . A numerical technique was tested for a onedimensional problem, having an analytical solution. Results of axially symmetric problem computations using 3D technique were compared with those of computations performed with 2D code. Test computations results, demonstrating efficiency and operability of the proposed technique are presented.
 AUTOMATIC CORRECTION FOR 2D GRID FRAGMENTS IN D COMPLEX WITH MIXED CELLS GIVEN R.A. Barabanov, V.I. Budnikov, O.I. Butnev, V.I. Delov, O.K. Loginova, V.A. Pronin, V.V. Sadchikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 6067.
The paper describes a technique for values recalculation in mixed cells under global correction of 2D Lagrangian grid fragments. The results are presented for test calculations of the problem on perturbation growth at a shock wave transition across the interface between two different materials. On linear and nonlinear stages of perturbation growth the computational results are compared with the results obtained by MEDUZAP codes.
 A SPLITTING SCHEME FOR NUMERICAL SOLUTION OF KINETIC VLASOV EQUATION A.I. Golubev, T.G. Sysoeva VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 3. P. 6871.
A finitedifference method for solving Vlasov equation, based on a new scheme of coordinate by coordinate splitting is presented. When constructing a numerical algorithm a scheme for splitting kinetic equation based on substitution of multidimensional transfer equation for a sequence of onedimensional transfers in each direction and twodimensional rotations is used and in addition to that Maxwell equations are splitted. For solving onedimensional transfer equations at the stage of accounting space gradients effect on the distribution function the scheme, using cubic spline interpolation is therewith applied. At the stage of accounting the electric field component effect on the distribution function a monotonous nonlinear Aloyan and Dymnikov scheme is used. To take into account magnetic field effect a special interpolation scheme, in which magnetic field does not change kinetic energy of plasma, is applied. Efficiency of the scheme under consideration is exemplified by the problem on numerical simulation of Landau jumping in heated collisionless plasma.
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