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25 January 2002, Volume 19 Issue 1 Previous Issue    Next Issue

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COMPUTING METHOD OF STOCHASTIC DIFFERENTIAL EQUATION AND IT'S APPLICATION LIU Xiao-qing, WU Sheng-Chang 2002, 19(1): 1-7.  Abstract ( )   PDF (288KB) ( )   Construction of discretization schemes, convergence principle, strongly convergent scheme and weakly convergent scheme for stochastic differential equations as well as computing method of jump stochastic differential equation are presented. Related partial differential equations are solved by probability method. Finally several examples in application are given.

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GROUP IMPLICIT METHOD FOR THE NONLINEAR HEAT CONDUCTION EQUATION AND NUMERICAL EXPERIMENTS ZHANG Bao-lin, LU Jin-fu, TAO Ying-xue, DU Zheng-ping 2002, 19(1): 8-12.  Abstract ( )   PDF (160KB) ( )   By using Saul'yev asymmetric schemes, the group implicit method is developed for the nonlinear heat equation appearing in laser physics, which has the obvious property of parallelism. Numerical experiments show that the new method has the similar accuracy with the known implicit method, and the numbers of iteration in both cases are nearly the same.

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ITERATIVE METHODS FOR SYMPLECTIC ALGORITHM OF WAVE EQUATION JIANG Chang-jin 2002, 19(1): 13-16.  Abstract ( )   PDF (140KB) ( )   By using the central difference quotient operator for (∂2)/(∂x2) and the diagonal Padé approximation of exp t, two kinds of symplectic schemes which have accuracy O(Δx2+ Δt2l) and O(Δx4+ Δt2l), respectively, can be attained for wave partial differential equation. Two iterative methods are described for the linear systems formed from the above schemes. Their conditions of convergence are given for l=1,2,3,4. The numerical experiments demonstrate that the symplectic algorithm have efficiency and both methods are convergent.

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KINETIC FLUX VECTOR SPLITTING METHOD BASED ON MAXWELL-BOLTZMANN DISTRIBUTION FUNCTION SHI Wei-ping, GENG Ai-fang, HUANG Ming-you, HU Shou-xin 2002, 19(1): 17-22.  Abstract ( )   PDF (207KB) ( )   The kinetic flux vector splitting method is combined with the two-time-step algorithm to simulate the inviscid ideal gas flow. The flux vectors of the equation are split on the basis of the local equilibrium Maxwell-Boltzmann distribution. Three 1-D standard test cases including shock waves, contact discontinuities and rarefaction waves are presented and compared with the exact solution.

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MULTIGRID SOLUTIONS FOR THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN ARTIFICIAL COMPRESSIBILITY FORMULATION YUAN Li 2002, 19(1): 23-29.  Abstract ( )   PDF (289KB) ( )   The full approximation storage (FAS) multigrid algorithm is applied in conjunction with the artificial compressibility method to accelerate steady solutions of the 3D incompressible Navier Stokes equations. Neumann boundary conditions in terms of the solution correction are implemented on the coarse grid when solving the coarse grid equations. The basic scheme used is the diagonalized approximate factorization scheme, and the spatial difference for inviscid fluxes adopts both MUSCL scheme and symmetric TVD scheme respectively for comparing. The performance of the present method is studied for the entry flow through a 90° bent square duct and the flow past an inclined prolate spheroid with an axes ratio of 4:1. It is found that the proposed multigrid method can save the computing time by at least half, and that MUSCL scheme is slightly better than TVD scheme in resolving the flow structures.

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GENERAL SYMMETRY AND RADIATIVE DIRECT EXCHANGE AREA SHEN Jiu-bin, LI Ben-wen, CHEN Hai-geng 2002, 19(1): 30-33.  Abstract ( )   PDF (232KB) ( )   Four basic types of integration of radiative exchange area are generalized using general symmetry and applied to ten kinds of computation.The kinds of partial blocks of the matrix of radiative direct exchange area are analyzed,and the whole matrix is classified into four types of partial areas.Utilizing general symmetry,the quantitative expressions for the computation reduction of the direct exchange area of both three dimensional and two dimensional systems are presented.

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EFFECTS OF SPHERICAL MIRRORS ON WAVEGUIDE FEL OSCILLATORS WANG Yuan-zhang 2002, 19(1): 34-36.  Abstract ( )   PDF (116KB) ( )   For the system in which the cylindrical mirrors of a hole-coupling plane waveguide free electron laser (FEL) oscillator are replaced by spherical mirrors, analytic estimation and numerical simulation are made respectively. It is shown that for the problem at hand, the influence on FEL by the mirror replacement is quite little.

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COMPENSATION FOR COMPTON SCATTER EFFECTS IN Tl-201 SPECT QIAN Lin 2002, 19(1): 37-42.  Abstract ( )   PDF (219KB) ( )   A method based on the Compton scatter theory is derived to compensate the effects of single and double scattering in Tl-201 SPECT.The scatter medium is divided into small volume elements and the scatter counts contributed by such a volume element are obtained by integrating the number of photons scattered by all electrons within the element.The scatter probability from an electron is determined by the Klein-Nishina formula.The counts are then assigned to the detector bin that is the projection point of the center of the element.In this way the singularity in calculating the scatter counts near a point source is eliminated.The main approximation is the finite volume of the element and the limited range of scatter medium included in the calculation.In spite of the approximation,the calculated scatter line source response function and scatter-to-primary ratio agree reasonably with those from Monte Carlo simulation and the computation time is shortened 40 times.

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NUMERICAL SIMULATION OF ELECTROMAGNETIC FIELD BY THE FINITE ELEMENT AND BOUNDARY ELEMENT METHODS IN THE SOFT-CONTACTING BILLET MOLD HUANG Jun-tao, HE Ji-cheng 2002, 19(1): 43-50.  Abstract ( )   PDF (299KB) ( )   The whole process of the numerical simulation of electromagnetic field in the liquid steel inside the soft-contacting billet mold is presented by FEM (Finite Element Method) and BEM (Boundary Element Method). Whitney edge element FEM based on tetrahedral elements, the discretization of H-Φ equation and boundary integration equation is mainly explained. By connecting FEM and BEM, it needs less work and time to the calculate the electromagnetic field. Numerical simulation program of three-dimensional electromagnetic field is exploited and the solution is proved to coincide with the fact.

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THE MODIFICATION OF FDTD METHOD IN THE COMPUTATION OF ELECTROMAGNETIC FIELDS IN SOFT-CONTACT CONTINUOUS CASTING QIAN Zhong-dong, LI Ben-wen, WANG En-gang, HE Ji-cheng 2002, 19(1): 51-56.  Abstract ( )   PDF (219KB) ( )   The Gandhi's scaled-frequency FDTD (finite-difference time domain) method for the computation of electromagnetic fields of low frequency is modified, which is adaptable to the numerical computation of soft-contact mould. The computational results for the simplified model agree well with the analytical solutions.

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TWO-DIMENSIONAL NUMERICAL SIMULATION OF LASER-IRRADIATED GOLD DISK TARGETS DUAN Qing-sheng, CHANG Tie-qiang, ZHANG Wei-yan, WANG Guang-yu, WANG Chong-ji, ZHU Shao-ping 2002, 19(1): 57-61.  Abstract ( )   PDF (227KB) ( )   A three-dimensional ray-tracing method for laser propagation in plasma and an algorithm of heat flow for electronic conduction are briefly described.A convenient calculation scheme for solving the non-equilibrium Pn equations is also presented.By using these methods and the newly developed LARED-H code,the two-dimensional simulations for the laser-irradiated gold disk and ring target are preformed.The reasonable two-dimensional behaviors of the target plasma are obtained.

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THE SYMPLECTIC METHOD FOR SOLVING THE LINEAR INHOMOGENEOUS CANONICAL EQUATIONS IN1-DIMENSIONAL INTENSE FIELD MODEL LIU Xiao-yan, LIU Xue-shen, ZHOU Zhong-yuan, DING Pei-zhu 2002, 19(1): 62-66.  Abstract ( )   PDF (175KB) ( )   For an intense field model, the time-dependent Schrødinger equation with initial and boundary conditions can be discretized into the inhomogeneous linear canonical equation by substituting the symmetric difference quotient for the partial derivative. As the general solution of its homogeneous equation and the particular solution of the inhomogeneous equation can be generalized by the symplectic transformation, it is a reasonable numerical method to use the symplectic scheme. To prove its utility, a simple example is described using the symplectic scheme and RK method, and compared with the exact solution. The results show that the solution using the symplectic scheme can preserve the intrinsic properties of the equations after a long evolution, but RK method cannot.

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THE EFFECT OF VECTOR FISSION SPECTRUM AND MATRIX FISSION SPECTRUM ON THE CRITICAL CALCULATION DENG Li, LIU Rui-lan, XIE Zhong-sheng 2002, 19(1): 67-72.  Abstract ( )   PDF (225KB) ( )   When the fission reaction happens in neutron transport calculation,the energy of the fission neutron can be usually determined by the fission spectrum.Since the coefficient of the spectrum type depends on the incident neutron energy,the multigroup neutron fission spectrum should strictly be a matrix form.In general transport calculation,the 235U vector fission spectrum is usually chosen as the standard fission spectrum.In order to make clear what kind of effect will be produced after this treatment,the Monte Carlo method and the multigroup P3 Monte Carlo neutron transport code MCMG are used to analyze the difference between two types of fission spectrums.By comparison the results with MCNP code,it is certain that the difference exists,but it does not have any effect on the correction of the calculated results.At the same time,the calculation results of the different neutron cross section libraries have been compared.

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COUPLED FINITE ELEMENT AND WAVELET BOUNDARY SPECTRAL METHOD FOR SOUND-STRUCTURE INTERACTION ANALYSIS OF AXISYMMETRIC BODIES WEN Li-hua, ZHANG Jing-mei 2002, 19(1): 73-76.  Abstract ( )   PDF (186KB) ( )   A spectral method in which wavelets are used as the basis functions is developed for solving acoustic and coupled structural-acoustic problems.On the basis of axisymmetric boundary integral formulation for axisymmetric bodies with arbitrary boundary conditions,the boundary quantities are expanded in wavelet series along the generator of the body,and a wavelet spectral formulation for solving acoustic problems of axisymmetric bodies is derived.Then, coupled wavelet spectral and finite element method is formulated for solving sound-structure interaction of axisymmetric elastic bodies with arbitrary boundary conditions.In this coupled method,a three-dimensional formulation is reduced to a one-dimensional one along the generator of the body.The coupled system is solved using the superposition principle for all the terms of Fouries series.The analysis of a submerged structure is performed.The comparisons of results based on the new technique with coupled finite element and boundary element methods are presented.Numerical solutions are given which show the fast convergence and the high accuracy.

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A HYBRID ALGORITHM APPLIED TO THE DESIGN OF DIFFRACTIVE OPTICAL ELEMENTS USED IN UNIFORM ILLUMINATION LI Tao, FU Shao-Jun, WANG Wei, XU Jun-zhong, LI Yong-ping 2002, 19(1): 77-80.  Abstract ( )   PDF (190KB) ( )   A hybrid method which collects the advantages of both iterative method and optimization method is introduced.This method is adopted in designing the diffractive optical device used in target illumination of ICF system,and better design results are obtained.The diffractive efficiency is up to 97.5%,the mean square error is 0.026 and the focal plane profile has an perfectly flat top.

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IDENTIFICATION OF CONSOLIDATION PARAMETERS OF SOILS BASED ON FUZZY THEORY LI Shou-ju, LIU Ying-xi, WANG Deng-gang, LIU Yu-jing, HE Xiang 2002, 19(1): 81-85.  Abstract ( )   PDF (223KB) ( )   Based on the fuzzy theory, the fuzzy identification algorithm of the soil consolidation parameters is set up according to the measured pore water pressure posited in the inner soils. The subordinate functions are also built in accordance with the statistic charactersistics of the observed pore water pressure. The fuzzy objective functions and the subordinate functions with fuzzy restriction are established too. Based on the information theory, the influence of uncertainty of the observed information and the uncertainty load to the identified results is studied. The research makes known that the identified results are still uncertain by making use of the above proposed identification algorithm.

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NUMERICAL PARALLEL COMPUTING OF UNBALANCED STIFF EQUATIONS IN DISTRIBUTED MEMORY ENVIRONMENTS LIU Jie, HU Qing-feng, HAN Guo-xing, CHI Li-hua 2002, 19(1): 86-88.  Abstract ( )   PDF (149KB) ( )   Unbalanced Stiff equations are used to simulate the nonequilibrium phenomena of radiation.The parallelism of the numerical computation is analyzed and a kind of load balancing method is given.In order to increase the data locality, a sequencing computation method in multi-processors is also given.With the corresponding parallel algorithm of the simulation,the results testified on the workstations are provided and discussed.

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ENHANCEMENT AND EVOLUTION OF SOLITARY WAVES EXCITED BY A LOCALIZED EXTERNAL SOURCE MENG Lu, LU Ke-li 2002, 19(1): 89-94.  Abstract ( )   PDF (247KB) ( )   By using a perturbation method, a forced mKdV equation is derived from the so-called quasi-geostrophic vorticity equation, and time evolutions of mass and energy of the mKdV solitary waves are discussed. Finally, numerical solutions of the forced mKdV equation are obtained by using the pseudo-spectral method. The calculation results show that the features of the mKdV solitary waves excited by localized external source are closely related to the detuning parameter α and the strength of the external source. The external forcing source in a forced mKdV system can excite larger amplitude and more instable disturbances than those in a forced KdV system.