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25 March 1991, Volume 8 Issue 1 Previous Issue    Next Issue

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PRECONDITIONAL METHOD FOR SOLVING THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS Zhao Jinbao, Sun Jianan, Zhang Jili, Zhang Wanshun 1991, 8(1): 1-10.  Abstract ( )   PDF (554KB) ( )   A new artificial compressibility method is discussed. It is a preconditional method presented by E. Turkel. We calculated the cavity flow model by explicit scheme and diagonalized implicit approximate factorization splitting scheme and compared with Chorin's artificial compressibility method. Final results show the preconditional method can relax restrict for the time step and Reynolds number and accelerated convergence.

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QUALITATIVE ANALYSIS TO A CLASS OF DELAY-COMPETITION SYSTEMS Yu Yuanhong, Huang Weizhang 1991, 8(1): 11-18.  Abstract ( )   PDF (435KB) ( )   In this paper the qualitative analysis of a class of Lotka-Volterra competition systems with continuous time delays are given. First, we discuss the stabilities of the systems. Then using Hopf's bifurcation theorem and Birkhoffs theorem we show that the delay-induced-instability can lead to appearance of stable limit cycles and that the systems may have recurrent solutions. Finally, some numerical examples are given in order to illustrate the results mentioned above.

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ON THE SERIOUS VARIATION OF NUMBERS OF PCG ITERATIONS CAUSED BY INITIAL GUESSES Lei Guangyao, Ma Zeyi 1991, 8(1): 19-22.  Abstract ( )   PDF (300KB) ( )   It was shown in literatures of the preconditioned conjugate gradient (PCG) that the initial guess gives little influence upon the number of PCG iterations when the stopping criterion requests to reduce the residual norm by a factor. However, the examples reported here show that using a zero initial gress or different random initial guess causes the number of PCG iterations varies seriously. Moreover, the number of iterations still varies seriously for the different parameter of the modeb when the same random initial guess is used. This variation should be avoided since it may cause confusions when different methods are compared. This paper shows that if the preconditioner is given, the series {rk} determined uniquely by the linear systems provided a zero initial guess is used. To avoid the serious variation in the number of PCG iterations, using the zero initial guess is a good choice.

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ANALYTICAL CONTINUATION METHOD FOR EVALUATING HIGHLY OSCILLATORY INTEGRALS Lo Bingbing, Wang Zhongxin, Chen Xuejun 1991, 8(1): 23-29.  Abstract ( )   PDF (427KB) ( )   The analytical continuation method is used for evaluating efficiently and accuratyintegrals, such as∫0xr2χ1(kr)χ1,(k'r)χL(pr)dr, where χ1(x) can be a spherical Bessel function jl(x), or a spherical Neumanm function nj(x). In particular, a practical program based on the method mintioned above has been made and its results show that the present method is very efficient and highly accurate.

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MONTE CARLO CALCULATION OF THE ENERGY SPECTRUM OF GAMMA RAYS EMITTED IN THE THREE PHOTON ANNIHILATION OF POSITRONS AND ELECTRONS Cheng Jinrong, Xu Qiang 1991, 8(1): 30-36.  Abstract ( )   PDF (386KB) ( )   In this paper, the Monte Carlo method is used to calculate the energy spectrum of gamma rays emitted in the three photon annihilation of positrons and electrons. Our results are compared with the results of calculation obtained by QED and experiment. These three results mentioned above are in agreement quite well.

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Computation of Flows in a Channel with a Facing Step by Schwarz Alternating Method Zhang Linbo, Wang Ruquan 1991, 8(1): 37-46.  Abstract ( )   PDF (520KB) ( )   This paper presents some preliminary work on the application of Schwarz alternating method, combined with a multigrid solver, for solving the steady 2D viscous incompressible Navier-Stokes equations. The difficulty caused by the violation of the compatibility condition imposed on the normal velocity at the boundary, which arises when subdomain problems are not solved exactly at each iteration, is surrounded by adding artificial compressiblity constants to the continuity equation each time when a subdomain problem is to be solved. These constants permit to maintain the compatibility condition of the subdomain problems and one can easily show that they tend to zero when the iteration number tends to infinity (in fact, they can be expressed explicitly as functions of the iteration number and some geometrical parameters of the computational domain). Numerical experiences have been made for flows in a channel with a facing step.

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A NUMERICAL CALCULATE PROGRAM REALIZATION FOR BIPARTITION MODEL OF ION TRANSPORT AND ITS APPLICATION Wang Shiming, Bai Rongsheng, Zhu Qi, Luo Zhengming 1991, 8(1): 47-56.  Abstract ( )   PDF (537KB) ( )   A numerical Program is described. It can display the transport process of ions and the correspond cascade process in solids. It includes principle, physical models, calculation procedure and the range used. A newest nuclear scattering cross-section is used in this program. The Cub-Spline interpolation method is also used in order to raise calculation speed and precision. Some calculation results are given such as the range distribution, energy deposition, radiation damage distribution in semi-infinite medium by included ions with different energy.

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A BLOCK PRECONDITIONED CONJUGATE GRADIENT METHOD USING HIGH ORDER APPROXIMATE INVERSES Lei Guangyao 1991, 8(1): 57-67.  Abstract ( )   PDF (581KB) ( )   A fast method is presented to compute high order approximate inverses for multidiagonal banded matrices of strong pivot. It is based on several concepts such as the order of an element in a strong pivot matrix, the order matrix and the influence areas of elimination steps.Under the condition of strong pivot, this method can be applied to unsymmetric and indefinite matrices. Coupling with the block preconditioned conjugate gradient, it is used for the numerical solution of elliptic partial differential equations and similar problems. It is demonstrated by the computational experiments that the method reported here has a higher efficiency in computations, comparing with similar methods.

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UPPER BOUND OF ‖A-1‖∞ AND EQUIDIAGONAL DOMINANCE Hu Jiagan 1991, 8(1): 68-78.  Abstract ( )   PDF (560KB) ( )   A simpler and more concrete estimate of the upper bound of ‖A-1‖∞ than those in previous papers is given, when A is an H-matrix and the equidiagonal dominant matrix is defined.We prove that if A is an equidiagonal-dominant M-matrix with equidiagonal-dominanceδ|i.e.|a11-||a11|=δ,∀i),则ρ(A-1)=‖A-1‖x=(A-1)ij=1/δ,∀i, By use of equidiagonal-dominant matrix the upper bound of ‖A-1‖x for any H-matrx may be found. Several interesting examples are given to illustrate our theorems.

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NUMERICAL SOLUTION OF THE FOKKER-PLANCK EQUATION Xing Jingru, Zhang Shufa 1991, 8(1): 79-87.  Abstract ( )   PDF (499KB) ( )   In order to study nuclear fission by means of diffusion model we have to solve Fokker-Planck equation. In this paper we present a relevant numerical calculation method of implicit difference. For the nuclear system with viscosity the physical quantities in relation to fission dynamics are calculated, for example, the density distribution, the fission rate, the mean kinetic energy at scission point and diffusion time from saddle point to scission point etc. The results are compared with kramers'stationary analysis solution which is valid for the large viscosity. The comparison and the test of normalized constant indicate that our calculation results are exact.

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THE CALCULATION AND THE MAIN FEATURES OF η<0 COULOMB WAVE FUNCTION Fang Dufei, Wang Yansen, Huang Fayang, Shi Wei 1991, 8(1): 88-94.  Abstract ( )   PDF (392KB) ( )   A approach of the calculation for the regular Coulomb wave function Ft (η,ρ) (η<0)and its main features depended on η,l and ρ are described. A example about their applications to integral calculations in electron-ion collision is given.

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A LAX-WENDROFF TYPE SCHEME WITH PREDICTOR-CORRECTOR Xu Guorong 1991, 8(1): 95-101.  Abstract ( )   PDF (404KB) ( )   In this paper a Lax-Wendroff type scheme with predictor-corrector is presented for solving the hyperbolic equations of fluid flow. The predictor solutions without introducing nonphysical oscillation are obtained by the method of flux vector splitting. The numerical flux of the corrector step is an anti-diffusive term, on which contraints are imposed to decrease the oscillation. Numerical experiments are presented to illustrate the performance of our proposed scheme.

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MONTE CARLO METHOD FOR SOLVING STOCHASTIC NONLINEAR EQUATIONS Gong Ye 1991, 8(1): 102-104.  Abstract ( )   PDF (193KB) ( )   It is suggested that the Monte Carlo method may be used to solve stochastic nonlinear equations. The practice proves that not only the results are highly satisfactory, but also the method is time-saving.

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THE MONTE CARLO SIMULATION OF MULTIPRODUCTION IN THE SOFT HADRONIC COLLISIONS Lu Jingfa, Chen Zhijiang 1991, 8(1): 105-109.  Abstract ( )   PDF (376KB) ( )   To compute the multi-particle productions in the Meson-Meson.Meson-Hadron, Hadron--Hadron and electron-positron reactions, a unified Monte Carlo simulation was made. The routine has been examined practically in the reactions mentioned above with DPM model in the intervals of 20-200 Gev. It is easy to reform it for another model.