Archive

25 June 1991, Volume 8 Issue 2 Previous Issue    Next Issue

---

For Selected:

Download Citations EndNote Ris BibTeX

Toggle Thumbnails

Select

SOLUTION OF THE GROUND STATE OF LITHIUM BY HARTREE-FOCK FINITE-ELEMENT METHOD Shi Aimin, Ding Peizhu 1991, 8(2): 111-121.  Abstract ( )   PDF (555KB) ( )   The energy of the ground Li-atom have been computed with the Hartree-Fock finite-element method. The relative error of the HFFEM result and HF limit value is-4.1×10-4. After considering correlative correct, the relative error of HFFECM value and experimental value is-4.9×10-4.

Select

A CLASS OF POLYNOMIAL COLLOCATION METHODS WITH SECOND DERIVATIVE FOR SOLVING STIFF ORDINARY DIFFERENTIAL EQUATIONS Li Linzhong, Chu Zhongwu 1991, 8(2): 122-130.  Abstract ( )   PDF (457KB) ( )   In this paper, a class of polynomial collocation methods with the second deriva live is derived for efficient integration of stiff systems. The methods are of one-step type, and the numerical solutions at m-point can simultaneously be obtained for each application of the formulas. It is shown that this class of methods is of order 2m+1 and the stability is analysed.

Select

ELECTRONIC STRUCTURE AND LUMINESCENCE OF BaF2 CRYSTAL Yang Jinlong, Xia Shangda, Wang kelin, Shi Chaoshu 1991, 8(2): 131-136.  Abstract ( )   PDF (382KB) ( )   The electronic structure and luminescence of BaF2 crystal are investigated using both self-consistent one-electron nonrelativistic Hartree-Fock-Slater and relativistic Dirac-Slater discrete variational-local density functional methods with an embedded cluster model. The energy levels, densities of states and spin-orbit coupling energy were obtained in good agreement with the experimental results. We verified that the fast luminescence components are the transitions of electrons from the F-(2p) valence band to the cation Ba2+(5p3/2) level, and pointed out that the necessary condition that the energy difference between the valence band and the core band must be smaller than the energy gap, for observing the fast luminescence components, is satisfied.

Select

STOPPING TEST OF ITERATIVE METHODS FOR SOLVING PDE Wang Bangrong 1991, 8(2): 137-148.  Abstract ( )   PDF (607KB) ( )   In order to assure the accuracy of the numerical solution of the iterative method for solving PDE, the stopping test is very important.If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method x(s+1)=Gx(s)+K for solving PDE is proposed in this paper. Several numerical examples are given to illustrate the applications of the stopping test formulas.

Select

THE λ-SCHEME AND ITS IMPROVEMENT Zhou Hong, Liu Ruxun 1991, 8(2): 149-156.  Abstract ( )   PDF (395KB) ( )   In the paper, an improvement λ-type scheme is proposed based on characteristics idea in order to overcome the strong dispersive effect or nonlinear instability of the original λ-scheme. Furthermore, the numerical simulations of two models of ID computational fluid dynamics problems by using the improvement scheme are given, and the numerical results are satisfactory.

Select

SOME MONOTONIC DIFFERENCE SCHEMES FOR CONNECTION-DIFFUSION EQUATIONS Lu Jinfu 1991, 8(2): 157-164.  Abstract ( )   PDF (427KB) ( )   With the varieties of the cell Reynolds number,We analyse the properties of the upwind scheme, the Samarskii Scheme and the modified Dennis scheme for convection-diffusion equations. Three semi-implicit schemes which are unconditionally stable and monotonic are present by those schemes. Numerical tests have shown these semi-implicit can be applied to solve for the steady fluid flow problems of high Reynolds.

Select

MATHEMATICAL SOLUTION OF TRANSPIRATION CONTROL EQUATION Gao Wei, Yang Xueshi 1991, 8(2): 165-173.  Abstract ( )   PDF (495KB) ( )   A solution of transpiration control equation is investigated in this paper. It is found that the equation can be classified as the classic heat transfer equation under certain conditions by means of variable alternation and then the analytic solution can be obtained. A numerical calculation of the analytic solution by a computer has proved the existence, uniqueness and stability of the solution. The theoretical problem of this sort of control system applied in the engneering is preliminarily ascertained. A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one. Because of limitation of the difference method, the steady numerical solution can be gotten in the region surrounded by R=0, BT=0 and R·BT=βτ/4h. The main conclusion of reference [2] is verified again.

Select

CALCULATING ELASTIC SCATTERING CROSS-SECTION OF LOW ENERGY ELECTRON BY PARTIAL WAVE METHOD Tan Zhenyu, Qiu Peiyoung, He Yancai, Wang Xinlei 1991, 8(2): 174-182.  Abstract ( )   PDF (471KB) ( )   Based on the work of Pendry, a Partial wave method of combining Hartree approximation with Hartree-Fock approximation is proposed for calculating elastic scattering cross-section of low energy electron. That method not only save computer CPU time, but extend Pendry's to a few keV-eneryg region. The elastic scattering cross-sections of element Be, C, Al, Cu are calculated and compared to Rutherford cross-section. The present method has been applied to investigation of low energy electron scattering in solids. A flow chart of calculating elastic scattering cross-section of low energy electron is given.

Select

A MONTE CARLO SIMULATION FOR LOW ENERGY ELECTRONS SCATTERING IN THE SAMPLE Xu Shuyan, Chen Shiping 1991, 8(2): 183-188.  Abstract ( )   PDF (338KB) ( )   A Monte Carlo simulation for low energy electrons scattering in the sample is presented in this paper. Since the particular features of the physical assumptions and the reaction mech anism, a method which combine the next-event estimator with the last-event estimator is employed. The results are satisfactory.

Select

NUMERICAL CALCULATIONS OF A KIND OF SPECIFIC SINGULAR BOUNDARY VALUE PROBLEMS Long Yongxing, Ding Ning, Qiu Xiaoming 1991, 8(2): 189-195.  Abstract ( )   PDF (415KB) ( )   A kind of singular boundary value problems for second order systems with a singularity at the origin and a non-normal singularity at the resonance layer are solved by means of the three-point difference method. Comparing with the method proposed by Ross et al.,[1] the present method is not only computationally simpler and more distinct but also can save much computer time. Our numerical results are in agreement with those given in Ref. 1.

Select

ORDER MATRIX AND ITS APPLICATION TO SEVERAL TRADITIONAL PRECONDITIONING METHODS Lei Guangyao, Zhang Shifeng 1991, 8(2): 196-202.  Abstract ( )   PDF (460KB) ( )   Using the concepts of element order and order matrix, some practical problems are discussed in which the traditional preconditioning methods ICCG and MICCG are adopted. If the fill-in number is fixed, why the method of ICCG(s,t) becomes the most efficient when (s,t) is successively (1,1), (1,2), (1,3), (2, 4), (3, 5),..? Why the number of iterations didn't decrease when m is larger than 3 for MICCG(m)? Is it possible to improve the fill-in method of MICCG? Is it always true that MICCG is better than ICCG? It tries to give a preliminary discussion on these problems in here. From the way of high order approximate LU decomposition, a method is introduced which improves and systematizes the ICCG and MICCG. An estimation of the condition number of ICCG is given based on the discussion of the order matrix for the error matrix. It is also pointed out that there was a trouble in selecting the parameter for MICCG. A reasonable way to select the parameter is given. Thus the number of iterations of MICCG decreases when the order of MICCG increases.

Select

A NEW IMPLICIT TVD SCHEME AND ITS APPLICATION TO SNS EQUATIONS Song Songhe, Wang Ruquan 1991, 8(2): 203-210.  Abstract ( )   PDF (391KB) ( )   Based on the theory of Sweby an implicit TVD scheme is obtained. The new method is first-order accurate with a truncation error of O The efficiency of this new scheme is demonstrated by some numerical computations of single Burgers equation and two-dimensional SNS equations.

Select

THE ENTROPIC INCREASE OF THE PLATE DRIVED BY EXPLOSIVE Liu Eryan, Wang Yuanshu 1991, 8(2): 211-215.  Abstract ( )   PDF (279KB) ( )   The entropic increase of a plate drived by explosive has been researched in one dimension system. Usually. The high explosive is contact with a plate immediately. There is the increase entropy of in the plate resulting from the interaction of a detonation with the plate, while increasing its kinetic energy.The rather idealized problem of detonation products initially at CJ state that expands in one dimension into a void and then accelerates a plate has been analyzed in mathmatical detail. It is believed that the technique described in this report can decrease the enlropic increase and increase some kinetic energy of the plate by choosing the proper length of void and thickness of the plate.

Select

COMPUTER AIDED DESIGN OF ELECTRON BEAM DEVICE FOR GUNS AND IMEAGE TUBES Yang Guowei, Guan Yonggui 1991, 8(2): 216-224.  Abstract ( )   PDF (528KB) ( )   Based on the finite difference method and the statistical theory of thermal electron emission, a set of computing and plotting programs using to computer aided design of electron beam device for electron guns and image tubes has been written in FARTRAN77 running on MV/8000 digital computer, and a good agreement between calculated result and that measured or given in ref has been obtained, This paper presents some numerical methods, such as optimization of Lagrange's interpolation function, determination of the optimum image plane using the statistical radius of the Airy disk, the tracing methods of equipotential lines and ion trajectories and so on. and some examples of the practical application, such as calculation and design for guns and image tubes, and analysis of the ion feedback in image tubes has been given.