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NUMERICAL STUDY OF PARALLELIZATION ALGORITHMS FOR 3-D NEUTRON DIFFUSION AND TRANSPORT CALCULATION WITH SATURN COMPLEX ON MULTIPROCESSORS

A.V. Alekseev, I.D. Sofronov, L.P. Fedotova, R.M. Shagaliev
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 38-39.

      This work considers the parallelization algorithms for 3-D group neutron diffusion and transport calculations on distributed memory multiprocessors. These algorithms are implemented in SATURN complex intended for 3-D stationary and nonstationary neutron-nuclei interaction calculations and for neutron transport in group diffusion kinetic approximation.
      The parallelization algorithm for diffusion equation rests on splitting the system into subdomains using the iterative process for special type internal boundary conditions ensuring unconditional process convergence.
      The parallelization algorithm for transport equation is iteration-free and uses the pipeline type scheme with sequential loading of processors.
      The testing results for parallelization algorithms are given obtained on the domestic 8-processor MP-3 system and on western distributed-memory multiprocessors (up to 256 PEs) Cray T3D and IBM SP2.



COMPUTATIONAL DOMAIN PARALLELIZATION FOR THE CONTINUUM MECHANICS CALCULATIONS ON EIGHT PROCESSOR DISTRIBUTED MEMORY MP-3 SYSTEM

Yu.A. Bondarenko, O.A. Vinokurov, V.V. Zmushko, F.A. Pletenev, P.V. Rybachenko, V.A. Saraev, I.D. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 47.

      The report presented the results obtained with MIMGZA codes for the parallelization of 2-D gas-dynamics and heat conduction equations on the eight-processor MP-3 system. The computational domain is divided into subdomains in accordance with the number of processors. When the gas-dynamic equations are solved, the neighboring subdomains have the overlapping portions through which the processors communicate. The parallelization of 2-D heat conduction equation uses the pipeline algorithm arid the transposition algorithm. The results of two computations are given.



CONSTRUCTING THE DIFFERENCE SCHEMES FOR THE CALCULATION OF MULTIDIMENSIONAL-TIME-DEPENDENT ELASTIC-PLASTIC FLOWS BASED ON INTERCONVERSION LAW FOR KINETIC AND INTERNAL ENERGY

V.I. Delov, O.V. Senilova, I.D. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 47-48.

      The report proposed an approach to the construction of conservative differential-difference representations of equations describing nonstationary elastic-plastic flows in Lagrangian variables. The method is the further development of 2-D method for the generation of spatial approximations to the equations of motion in gas dynamics [1,2] for elastic-plastic media.
      In this work the matrix of kinetic energy determining the approximation technique for the pressure gradient is taken in the canonical form that is traditionally used in gas-dynamic codes.
      The report presented the difference formulas for the components of deformation rate tensor and the resulting difference approximations for the evaluation of derivatives with respect to the components of the stress deviator.
      The computational results were reported obtained with difference schemes where the grid distribution of quantities in time is taken like in “D” code [3] and the time derivative is approximated with the second order accuracy. The problem describing the elastic oscillations of membrane is taken to show unquestionable advantages of the resulting difference schemes as compared to the classical Wilkins scheme.
      1. Isaev V.N., Sofronov I.D. Construction of discrete models for gas-dynamic equations based on the interconversion law of kinetic and internal energies of continuum // Voprosy Atomnoy Nauki i Tekhniki. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. N 1(15). P. 3-7.
      2. Delov V.I., Isaev V.N., Sofronov I.D. Conservative and invariant differential-difference representations of gas- dynamic equations in cixisymmetric case // Ibid. 1987. N 1. P. 3-10.
      3. Dmitriev N.A., Dmitrieva L.V., Malinovskaya E.V., Sofronov I.D. A method for the calculation of 2-D gas-dynamic problems in Lagrangian variables // Theoretical Fundamentals and Construction of Numerical Algorithms in Computational Physics / Ed. by Babenko K.I. M.: Nauka, 1979. P. 175-200.



DEVELOPMENT OF MASSIVELY PARALLEL MULTIPROCESSORS BASED ON HYPERCUBE ARCHITECTURE

V.A. Novichikhin, A.V. Pastukhov, V.A. Gusev, A.M. Lyakishev, G.A. Popovidchenko, A.A. Runich, I.D. Sofronov, S.A. Stepanenko, V.N. Timchenko, A.A. Uzentsov, A.A. Kholostov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 60.

      The MIMD multiprocessor MP-X (various instruction threads over various data threads) consisting of 2x- processing elements is a functional module designed for parallel computations.
      The MP-X rests on the following concepts;
      — combination of the MP-X multiprocessor with the general purpose host computer Y allowing to combine the advantages of parallel, vector and scalar, processing when executing a program that contains non-parallelizable fragments;
      — adaptibility of connectivity structure to the algorithms of the applications to be run (program emulation of various interprocessor connections);
      — design modularity which allows to upgrade the performance according to the user demands a;nd simplifies the transition to new microprocessors and new message passing technologies;
      — hardware support of the routing algorithms to increase the efficiency of the interprocessor transfers;
      — higher failure tolerance level of MP-X due to redundancy;
      — orientation to the common programming languages with the support of parallel program development tools standard in this field.
      The most efficient applications for MP-X-Y include: multidimensional problems in computational physics, design computerization, image processing, artificial intellect and others that require a maximum possible number of operations for this class of Y computers.
      The concepts presented are used in MP-0, MP-3 models and serve the base for MP-7 project.
      The description is given for the component base of existing and future models of some MP-X, as well as the software used for the development of parallel codes. The results are given for some test problems on various types of similar computers including MP-0 and MP-3.
      The report was accompanied by the illustrations arid demonstration of operational models.



COMPUTER SIMULATION AT VNIIEF

I.D. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 63-64.

      Following issues were considered:
      1. A brief characterization of the codes developed in 1985-1995:
      - 1-D codes;
      - 3-D codes;
      - models for the processes considered.
      2. Some features of the developed computational technology:
      - inadequate performance of computers and requirements for the methods, computers and mathematicians;
      - a low number of cells, computational credibility, various computational techniques;
      - full-scale tests — a necessary component at the computational technology.
      3. Some requirements for the new technology:
      - more accurate models for physical processes;
      - user-independent computations;
      - convergence computations, computational validity;
      - mathematical testing;
      - development of new algorithms allowing a sufficient parallelization.
      4. Technical base:
      - multi-user computer network;
      - up-to-date state of computing base;
      - various classes of machines within the new ensemble of computers;
      - parameters of the desired supercomputer;
      - various ways for computerization.



PARALLELIZATION METHODS AND PARALLEL CODE FOR NUMERICAL CALCULATION OF 3-D HEAT CONDUCTION EQUATION ON DISTRIBUTED MEMORY SYSTEM. COMPUTATIONAL RESULTS OBTAINED ON MP-3 AND MEIKO SYSTEMS

I.D. Sofronov, B.L.Voronin, O.L. Butnev, A.N. Bykov, S.L. Skrypnik, D. Nielsen, Jr. D. Nowak, N. Medsen, R. Evans
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 64.

      Numerical calculation of 3-D problems requires the threshold computing resources provided by massively parallel distributed memory systems. A successful use of a high potential performance of such systems for the calculation of a single problem is only possible after the development of application programs supporting the parallel processing.
      The paper presents the results of the parallelization efforts for 3-D heat conduction equation. The basic method for numerical calculation of 3-D implicit finite-difference equations is the directional splitting. This method allows to reduce a complicated multidimensional problems to a collection of simpler problems that can be run on parallel processors.
      Two conceptually different approaches were developed for the organization of massively parallel computations. The first uses the decomposition of 3-D data matrix reconfigured at a timestep and is the development of the parallelization algorithms for the shared-memory multiprocessors. The second approach rests on nonreconfigurable decomposition of the 3-D data matrix.
      The resulting algorithms were implemented as a parallel code for massively parallel distributed-memory systems.
      The series of computations allowed the numerical studies of the parallelization efficiency for various techniques of the geometrical decomposition, for two modes of processor loading and depending on arithmetic execution/communications ratio.
      The quantitative estimates are given for the parallelization of the resulting algorithms obtained on MP-3 and Meiko systems.



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