MONTE-CARLO METHOD FOR MODELING LANDAU COLLISION INTEGRAL

N. V. Ivanov, Yu. K. Kochubey
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 3-14.

      Landau collision integral is approximated by the integral of Boltzmann collisions within the expanded phase. General approach to solving Boltzmann equation using Monte-Karlo method being similar to techniques of direct statistical modeling in sparse gas dynamics is described. Two schemes of modeling collisions in plasma are given. The proposed techniques are accompanied with numerical calculations.

E. S. Andreev, V. Yu. Gusev, M. Yu. Kozmanov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 15-18.

      The first order approximation scheme improvement techniques are considered which allow to gain necessary accuracy using more rough space grid. The results obtained are illustrated by examples.

Yu. I. Molorodov, G. S. Khakimzyanov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 19-27.

      The paper is devoted to the problems of developing a program system for generating curvilinear grids in simply connected regions of a complex form. The problems of constructing initial approximation for iterative techniques of computing node coordinates are discussed. Criteria are given which allow to estimate the quality of grids generated using different techniques and to select a most acceptable one.

V. E. Kondrashov, S. B. Korolyov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 28-33.

      The new iteration technique of computing eigenvalues of the general form matrix in ascending order of their moduli and eigenvectors corresponding to them is presented. Implementation and justification of this technique is brie у discussed and some possible applications are considered. Some changes of the algorithm allow to find eigenvalues in the reverse order. The technique is useful first of all for estimating the upper and especially the lower spectrum boundaries and appears to be too costly for the entire spectrum determination. This technique generalization for polynomials from scalar variable with matrix coefficients is given in the paper.

B. L. Voronin, A. M. Erofeev
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 34-36.

      Brief description of parallel computation arrangement for solving 3D heat conduction equation using orthogonal computational blосk-matrix grids is riven. Combination of the parallel region-by-region computation scheme with sweep parallelization is used. The efficiency of parallelization algorithms is numerically studied. Computations have been performed using 8 processor computer system MP-3.

G. P. Prokopov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 37-46.

      To obtain grids close to orthogonal ones (quasi-orthogonal grids) the functional regularization is implemented that is equivalent to adding elliptic functionals with quite small weight.
      For providing a grid nondegeneracy the functional discretization is performed similarly to the “variational barrier” technique proposed for the widely used functional representing Dirichlet integral for the inverse mapping.
      The functional minimization using the direct descent technique which doesn’t use the functional gradient permits to avoid numerical integration of Euler equation system (that would be quite bulky) and great difficulties when using numerical techniques such as splitting to solve it.
      The developed algorithm of the descent technique implementation for an arbitrary functional allows to restrict computations by functional calculation on a local pattern including grid nodes (in the case, when the functional integrand expression depends on its first derivatives).

I. D. Sofronov, E. L. Shnepov, A. S. Maksimov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 47-53.

      General description of the inquiry system intended for information servicing users of the VNIIEF collective information computer network is given. The system purpose, its main capabilities, functional structure and system operation logics are considered. The inquiry system operation showed that it successfully performs its functions.

V. V. Dremov, D. G. Modestov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 54-58.

      Variation equation of state brief description of which is done in the beginning of this paper have been applied for substituted methane compounds (di-chloromethane, chloroform and tetrachloromethane) melting curves calculation. The analog of Lindemann law has been used directly for these calculations, namely: packing factor η along the solidification curve remains constant.

S. M. Bakhrakh, E. B. Voronina, E. V. Ustinova, S. A. Shaverdov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 59-65.

      Numerical algorithm is developed describing in 2D geometry layer-by- layer burning front propagation at a velocity depending on local gas dynamic material parameters in each front point. The algorithm is based on the well known physical Huygens principle for wave front propagation. Test results are given, good agreement between the results obtained and exact solutions is demonstrated.

N. F. Gavrilov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 66-72.

      Polynomial application spline for constructing an implicit conservative scheme for the convective transport equation integration is described. The assumption of the desired solution smoothness with the first-order time derivative is successively implemented.

S. N. Egorov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 1. P. 73-77.

      The development of very large scale integration circuits (VLSIs) on the base of basic matrix chips (BMC) is a complex process involving a VLSI manufactures and its customer. VLSI customer is to develop schematic diagrams within the basis of BMC library elements and tests for production control over the integrated curcuits manufactured. The development of schematic diagrams and tests is usually carried out under the environment of the specialized system of computer-aided designing (CAD). Such system application for a large amount of VLSIs is not efficient.
      The paper considers VLSI CADs constructed from components of widely used lowcost computer-aided design systems. PCAD designing system and FLY DIGITAL DESIGN+ system of logical modeling are used as the CAD’s base. Additional program tools have been developed during VLSI CADs designing which solve the two main problems:
      - increase in modeling accuracy;
      - providing a possibility to prepare test sequences for control over the integrated circuits manufactured.
      Using this CAD system three types of VLSIs have been designed for the system of interprocessor communications in MP-3 multiprocessor, that have been successfully manufactured and tested.