Issue N^{o} 4, 1996 
PARALLELIZATION METHODS AND A PARALLEL PROGRAM FOR NUMERICAL SOLUTION OF THE 3D HEAT TRANSFER EQUATION USING DISTRIBUTED MEMORY COMPUTATIONAL SYSTEMS (CS). RESULTS OF NUMERICAL EXPERIMENTS ON MP3 CS AND MEIKO CS2
I.D. Sofronov, B.L. Voronin, O.I. Butnev, A.N. Bykov, S.I. Skrypnik, D. Nielsen, D. Novak, N. Medsen, R. Evans VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 34.
Results of a parallelization effort as applied to 3D heat transfer computations are described. The basic approach to numerical solution of the systems of 3D implicit finitedifference equations is the method of directionbased splitting. Two fundamentally different approaches to the organization of the massively parallel computations were developed. Parallelization efficiencies of the developed algorithms obtained on the MP3 and Meiko computational systems are reported.

SOLUTION PROPERTIES OF THE VARIATIONAL STEPBYSTEP OPTIMIZATION PROBLEM OF REDISTRIBUTION OF MESH POINTS ON A PROCESSOR LINE Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 57.
A numerical method of explicitdifferencescheme type with an ordered mesh point distribution between processors is considered as applied to a processor line. It is presumed that its parallelization involves a load balancing algorithm, when mesh points are transferred from one processor to its neighbor at each time step. Presuming that the computational time is different for different points and that it can vary with time, we set a variational problem of stepbystep computational time minimization with the account for processor load nonuniformity and time losses for both regular processor communication and exchange of mesh points between processors to balance their load. A complete mathematical analysis of this variational problem was carried out. Practical applicability of the results obtained is discussed.

EXPERIENCE IN THE DEVELOPMENT OF A PARALLEL PROGRAM TO SOLVE THE PROBLEMS OF MATHEMATICAL PHYSICS IN A DISTRIBUTED COMPUTING ENVIRONMENT A.M. Anikin, A.Yu. Bisyarin, I.A. Gorbatova, V.M. Gribov, A.V. Kim VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 810.
The authors developed basic means for parallel computations in localarea networks with different types of computers under the UNIX operating system. A set of such means enables parallel computations and debugging of new parallel codes meant for use on real distributedmemory multiprocessor computers. The interface of the applied programs on the basis of Berkly slots is written in the C language and implemented as a library of procedures.

IMPLEMENTATION OF THE PARTICLEINCELL METHOD ON DISTRIBUTEDMEMORY MULTIPROCESSORS V.A. Vshivkov, G.I. Dudnikova, M.A. Kraeva, V.E. Malyshkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 1115.
The results of developing a programming environment designed for different implementations of the PIC method are presented. This effort is part of the ASSY project (ASsembly SYstems). The project is aimed at the development of a metasystem to support the development of problemoriented programming environments. The PIC method is one of the benchmarks to test real capabilities of the ASSY technology.

NUMERICAL RESEARCH ON THE PARALLELIZATION ALGORITHMS FOR 3D NEUTRON DIFFUSION AND TRANSPORT COMPUTATIONS IN THE SATURN CODE ON MULTIPROCESSOR COMPUTERS A.V. Alekseev, I.D. Sofronov, L.P. Fedotova, R.M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 1623.
Parallelization algorithms for 3D group neutron diffusion and transport computations on distributedmemory multiprocessor computers implemented in the SATURN code are considered. We present the results of testing the parallelization algorithms on the homemade 8processor system MP3 and foreign distributedmemory multiprocessor systems (up to 256 processors) Cray T3D and IBM SP2.

DOMAINBASED PARALLELIZATION OF CONTINUUM MECHANICS COMPUTATIONS ON THE MP3 8PROCESSOR DISTRIBUTEDMEMORY COMPUTER I.D. Sofronov, Yu.A. Bondarenko, O.A. Vinokurov, V.V. Zmushko, F.A. Pletenev, P.V. Rybachenko, V.A. Saraev VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 2428.
Parallelization techniques for an explicit and an implicit difference scheme are described. The explicit scheme was used for multidimensional gas dynamics equations, and the implicit scheme, for the 2D heat transfer equation. Computational results are reported.

PARALLELIZATION OF AIRCRAFT NAVIGATION AND GUIDANCE ALGORITHMS V.B. Kostousov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 2933.
The problem known as the development of extreme correlation navigation systems is described. Algorithms to analyze spatial scenes and to compare the current image with the reference external field are discussed. The NAVIGATOR software package that uses parallel processes when modeling the navigation system is described.

STABLE SCHEMES FOR PARALLEL SUBDOMAIN COMPUTATIONS OF THE HEAT TRANSFER EQUATION B.L. Voronin, A.M. Erofeev VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 3437.
Some schemes for parallel subdomain computations are considered, including a scheme with a run parallelization algorithm proposed in a work by N.N. Yanenko. Issues of stability and accuracy of computations are studied and conclusions are made on the possible implementation of these schemes for massively parallel calculations.

FORTRAN GNS MOBILE PROGRAMMING SYSTEM FOR DISTRIBUTEDMEMORY MULTIPROCESSOR SYSTEMS L.A. Pozdnyakov, M.Yu. Khramtsov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 3842.
We consider possible approaches to the choice of the tools to develop effective mobile applications for parallel distributedmemory computational systems and the ways to implement such tools. We discuss the issues of improving the portability of the tools to describe the software and hardware configuration.

CHALLENGES AND PROSPECTS IN THE DEVELOPMENT OF PARALLEL PROGRAMS FOR CONTINUUM MECHANICS COMPUTATIONS WITH DYNAMIC COMPUTATIONAL LOAD BALANCING S. P. Belyaev, L. I. Degtyarenko, I. Yu. Turutina VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 4344.
Continuum mechanics computations with workload variations in time can involve dynamic load balancing by transfer of computational points from overloaded to underloaded processors. Possible redistribution of arbitrary points across processors results in the necessity of pointbypoint parallelization.

ALGORITHMS FOR AUTOMATIC COMPUTATIONAL LOAD REDISTRIBUTION S.P. Belyaev, I.Yu. Turutina VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 4548.
Parallel continuum mechanics computations with workload variations in time can involve dynamic load balancing by transfer of computational points from overloaded to underloaded processors. The algorithms for automatic point redistribution across processors do not need to be highly accurate, but it seems necessary for them to possess a number of properties, including simplicity of the computational procedure to determine the quantity of the points to be transferred with as little information as possible and local decision making during redistribution. It is presumed that each processor has received time step completion reports from its neighbors, including the processor time and the number of points that each neighbor can accept from this processor, by the time the algorithm is set in operation.

PROBLEMS AND METHODS OF DEBUGGING PARALLEL PROGRAMS A.O. Ignatev, A.A. Kalinin, V.K. Koryakin, A.I. Melnikov, L.S. Talantova, N.I. Shulepov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 4951.
An overview of problems and methods for parallel program debugging and monitoring on massively parallel distributedmemory MIMD computers is provided. Systems for active justintime debugging and postprocessing of data accumulated during program execution are considered. Some aspects of active debugging and postprocessing system implementation are discussed; some ideas on the functional structure of the debugging system are proposed.

PROGRAM DEBUGGING METHOD FOR MASSIVELY PARALLEL MACHINES V.V. Samofalov, A.V. Konovalov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 5256.
One of the ways to solve the problem of debugging parallel programs is to clearly understand the role of models in debugging and distribute debugging actions at several levels. The work introduces the notion of stagebystage debugging and describes its initial implementation to support this debugging technology.

THE METHOD AND PROGRAM TO DETERMINE THE COMMON VOLUME OF INTERSECTION OF TWO NONPLANARFACE HEXAHEDRONS ARBITRARILY LOCATED IN SPACE V. I. Delov, L. V. Dmitrieva, V. V. Sadchikov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 5761.
A method developed to solve the spatial problem on the existence of an intersection between two hexahedrons arbitrarily located in space and the way to find the common volume of their intersection, if any, is presented. The faces of the hexahedrons are represented as a set of four flat triangles with a common vertex in the geometric centers of the faces. The number of triangles that approximate the surface of the face can be easily replaced if necessary.

1D METHOD OF COMPRESSION AND BURNING IN INERTIAL CONFINEMENT FUSION PROBLEMS OF E.M. Antonenko, G.V. Dolgoleva, V.F. Ermolovich VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 6266.
A mathematical program, called ALF, to model fusion burning and compression characteristics is discussed. The models, the numerical method of their solution, and the numerical results of target performance simulations for the target proposed for use in the NIF laser project are presented.

CONSTRUCTING DIFFERENCE SCHEMES FOR 2D UNSTEADY ELASTOPLASTIC FLOW COMPUTATIONS BASED ON THE LAW OF MUTUAL CONVERSION OF KINETIC AND INTERNAL ENERGY V.I. Delov, O.V. Senilova, I.D. Sofronov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 6772.
An approach to the construction of conservative differentialdifference representations of equations to describe unsteady elastoplastic flows in Lagrangian variables is proposed. 2D axially symmetric motion of an isotropic elastoplastic medium is considered. Results of computations by a difference scheme of the second order of approximation in time obtained using the constructed differentialdifference equations of motion are reported.

NUMERICAL DECONVOLUTION V.E. Kondrashov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 7376.
A purely algebraic method of deconvolution is proposed, which differs from those based on some variational principles (regularization, quasisolution etc.).

RAYLEIGHTAYLOR INSTABILITY OF AN ACCELERATED THIN ELASTIC LAYER S.M. Bakhrach, G.P. Simonov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 7784.
Development of 2D and 3D perturbations of an accelerated thin elastic layer is studied analytically and numerically using the Lagrangian representation of the equation of motion. Approximated analytical solutions were produced for the nonlinear stage of the process in the space of an observer. Ratios for the increment of the perturbation growth and critical acceleration are provided. Perturbation development as a function of nondimensional parameters that determine the form of the initial perturbation is studied in detail for 2D perturbations. In particular it was found out that the strength changes the condition of boundedness of the solutions. The analytical solutions are compared with results of 2D and 3D computations using a complete system of equations of motion for an elastic medium. It is noted that the analytical solutions and the results of the numerical computations match each other. 3D perturbations of the elastic layer (at a sufficiently high shear modulus), as opposed to a liquid one, are shown to grow not faster than its 2D perturbations.

ON THE CONSISTENCY OF DAMAGE DESCRIPTION IN COMPUTATIONS ON COMPUTERS A.G. Ivanov VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 8588.
A number of works on the description of a space body penetrating the atmosphere of the planet are considered. A consistent description of the qualitative picture of the phenomenon can be produced using an integral damage criterion. The use of traditional materials strength criteria fails to provide correct description of the process under consideration.

HIGH RESOLUTION HYDRODYNAMIC USING ARTIFICIAL VISCOSITY Randy B. Christensen VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 8993.
We will present a method for obtaining highorder, nonoscillatory results for staggered mesh (velocities at cell boundaries), internal energybased hydrodynamics codes using a simple modification of the well known Artificial Viscosity technique. This method is derived by particular approximate Riemann solvers. The resulting method will be shown to deliver results comparable to such cellcentered, total energybased method as Flux Corrected Transport (FCT) and highorder Godunov schemes.

STRATEGIES FOR ADOPTING PARALLEL PROCESSING IN LARGE SIMULATION CODES Dale E. Nielsen VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 9497.
The highperformance computing community has seen a steady procession of different parallel computing architectures. For large application codes, the time required to change from sequential algorithms to parallel algorithms, or even change between parallel algorithms for different architectures is longer that the lifetime of individual parallel computers. Smooth transition strategies will be described which overcome this challenge, and the parallel machine characteristics defined which make these transition strategies possible. Slides providing material is presented.

PARALLELIZATION OF A 3D DETERMINISTIC NEUTRONICS CODE D. Barrett VANT. Ser.: Mat. Mod. Fiz. Proc. 1996. No 4. P. 98101.
The presentation describes a parallel code for solving neutron transport in 3D geometry: domain decomposition message passing. Measured time characteristics are given. A prediction is made for further development of these works.

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