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RUSSIAN FEDERAL
NUCLEAR CENTER -
ALL-RUSSIAN RESEARCH INSTITUTE
OF EXPERIMENTAL PHYSICS
 
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Issue No 1, 2008


APPLICATION OF MULTIGRID TECHNIQUES FOR SOLVING PARABOLIC EQUATIONS

M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 4-19.

New effective solution algorithm for parabolic equations based on multigrid technique is suggested which maintains virtues of implicit scheme — stability and accuracy. At the same time this algorithm allows to considerably reduce number of arithmetical operations on each time layer. Absolute stability of the suggested technique is theoretically proved by example of one-dimensional model problem. Accuracy of the technique is investigated by example of two-dimensional model problem. It is proved that for model problem solution obtained using the suggested technique differs little from solution for implicit scheme on explicit grid. Computations of one- and two-dimensional problems with continuous and discontinuous coefficients show good accuracy of the suggested technique.




COMPARISON OF DIFFERENT VARIANTS OF HIGH-FREQUENCY APPROXIMATION ON THE MODEL PROBLEM FOR MAXWELL’S EQUATIONS

A. L Golubev, N. A. Ismailova, V. A. Terekhin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 20-29.

Exact solution of Maxwell’s equations is compared on representative two-dimensional model problem with solutions of simplified equations derived from different variants of high-frequency approximation. Comparison shows that for the considered problem derivatives accounting by angle variables in high-frequency approximation equations essentially expands time fields of application of this approximation.




INVESTIGATION OF INFLUENCE OF SOME ARTIFICIAL VISCOSITY FORMS ON “ENTROPY TRACE” CHARACTER FOR NUMERICAL SOLUTION OF GAS-DYNAMICS EQUATIONS

A. M. Stenin, E. A. Solov’eva
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 30-41.

The paper considers the problem of errors reduction for values of quantities in entropy trace domain originating in computations of Lagrangian gas-dynamics problems conducted with the help of difference schemes of shock waves end-to-end computation.
Artificial mass diffusion, artificial impulse diffusion and artificial total energy diffusion are conservatively entered into gas-dynamics equations set in Euler coordinates. Formulas for velocity of artificial mass diffusion in continuity equations and for artificial viscosities in motion and energy equations in Lagrangian coordinates are derived from this equations set. In the case of cylindrical and spherical symmetry of flows tensorial artificial viscosity similar to physical viscosity is entered to the motion equation instead of scalar viscosity.
Methods of modification of obtained viscosity system by means of Hugoniot conditions on shock wave are considered which improve computation results in entropy trace domain.
Results of conducted test computations show high efficiency of new viscosity system concerning reduction of entropy trace for numerical solution of Lagrangian gas-dynamics equations.




DEBYE D3(x) FUNCTION APPROXIMATION IN 0 ≤ x < ∞ DOMAIN BY CLASS C2 FUNCTION

D. G. Gordeev, A. L Lomaykin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 42-50.

The paper presents results of fitting and realization of approximation expression for Debye D3(x) function in 0 ≤ x < ∞ domain. Approximation provides continuity up to and including the second derivative and computation time acceptable for application programs.




BI-LEVEL PARALLELIZATION IN MIXED MEMORY MODEL FOR COMPUTING GAS-DYNAMICS PROBLEMS IN TIM-2D TECHNIQUE

A. A. Voropinov, S. S. Sokolov, I. G. Novikov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 51-59.

The paper gives description of parallelization scheme for computing gas-dynamics problems subject to elastoplastic material properties using TIM-2D technique destined for solving problems of mechanics of continua on non-regular polygonal grids with arbitrary structure.
Three-level parallelization is realized for TIM-2D technique. On the first (upper) level computation parallelization over mathematical domains is realized in distributed memory model using messaging interface MPI. On the second level computation inside countable domain is parallelized for para-domains also using MPI (countable domain is splitted onto fragments by single-layer cell superposition). On the third (lower) level parallelization of counting loop iterations is realized in common memory model using OpenMP interface. These approaches can be used both together in different combinations and separately for computing the same problem.
The paper considers in detail parallelization algorithms on the upper and the lower levels. Different modes of parallel computation are described. Measurements of acceleration and efficiency of parallelization are given.




UNIFORM TASK CONTROL SYSTEM FOR HETEROGENEOUS COMPUTER COMPLEX

A. B. Kiselev, Yu. G. Bartenev, A. M. Vargin, S. N. Kiselev, S. I. Kolpakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 60-66.

Architecture and performance capabilities of uniform control system for calculating parallel applications on computers of RFNC-VNIIEF are described. System is created in order to organize centralized entry, test and task computation control in heterogeneous computer complex.




ON SOME STEREOTYPES OF PARALLEL PROGRAMMING

G. V. Baydin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 67-75.

Consistency of some working ideas of parallel programming is examined. Problems of computations against interchanges, optimal message size, optimality of nonblocking and cooperative operations are considered.




50 TH ANNIVERSARY OF FORTRAN: HISTORY, CURRENT STATE AND FUTURE

V. P. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 1. P. 76-89.

The paper is based on materials of the report represented on mathematical conference of RFNO-VNHTF in Snezhinsk in 2007.
Fortran can be described both very briefly and in considerable detail so this paper must be considered only as the author’s outline. The author hopes that the paper will attract attention to Fortran and at least reduce distrust and neglect undeservedly originated among programmers in respect to Fortran during the last two decades. Both officially published materials and information from Internet were used while preparing the paper. The author apologizes for possible inaccuracies.




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