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25 November 2005, Volume 22 Issue 6 Previous Issue    Next Issue

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Efficient Algebraic Methods for Two-dimensional Energy Equations with Three Temperatures GU Tong-xiang, DAI Zi-huan, HANG Xu-deng, FU Shang-wu, LIU Xing-ping 2005, 22(6): 1-8.  Abstract ( )   PDF (422KB) ( )   We developed a high performance algebraic solver for nonlinear systems discretized from two-dimensional energy equations with three temperatures by a nine point scheme.The main idea is to solve the system by an inexact Newton method and preconditioned Krylov subspace methods in the frame of PNK and JFNK methods.Numerical experiments show the efficiency of the algebraic solvers.It is shown that our PNK method is 6 times faster than the nonlinear block Gauss-Seidel method. The JFNK and PNK methods are also compared.

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A Difference Scheme for Two-dimensional Three-temperature Energy Equations and Numerical Simulations for Planar Targets YONG Heng, DUAN Qing-sheng, PEI Wen-bing, JIANG Song 2005, 22(6): 9-17.  Abstract ( )   PDF (437KB) ( )   A difference scheme for two-dimensional three-temperature energy equations in Cartesian coordinates is united with that in cylindrical coordinates.The LARED-H (laser radiation electron dynamic holehurm) code is extended to describe physical processes in both coordinates.Physical models are investigated for a line-focused target with different incident angles.Numerical results are given to describe the expanding process of target-plasma.

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A Class of Algebraic Multigrid Algorithms with Three-Dimensional Equal Algebraic Structures SHU Shi, HUANG Yun-qing, YANG Ying, YU Xi-jun, XIAO Ying-xiong 2005, 22(6): 18-22.  Abstract ( )   PDF (313KB) ( )   Two kinds of algebraic multigrid (AMG) algorithms with three-dimensional equal algebraic structures are constructed on the basis of a two-dimensional coarsing technique.The AMG method and the corresponding algebraic multigrid-preconditioned CG method are applied to elliptic boundary value problems with smooth coefficients and anisotropic problems.Numerical results show that the AMG algorithm is efficient and robust.

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A Jet Symplectic Algorithm for Euler-Lagrange Systems YU Hua-ping, WANG Shuang-hu 2005, 22(6): 23-30.  Abstract ( )   PDF (360KB) ( )   A jet symplectic algorithm for Euler-Lagrange systems is studied.It is shown that the discrete Euler-Lagrange (DEL) equation,which was given by the second author in 1998,has fundamental geometric structures that preserve along solutions obtained directly from the variatonal principle.It is shown that these difference schemes are jet symplectic and the Nother's theorem exists by which we give the definition of a discrete version,the momentum map.A numerical example in jet symplectic difference scheme is given.A comparison with other discretization schemes was made.

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Regularization of Nearly Singular Integrals in the Boundary Element Method for 3-D Potential Problems ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi 2005, 22(6): 31-36.  Abstract ( )   PDF (298KB) ( )   A semi-analytical integral regularization algorithm is applied to the evaluation of nearly strongly-singular and nearly hypersingular surface integrals in the boundary element method (BEM) for three-dimensional potential problems.The algorithm is available for linear triangular isoparametric elements.The algorithm can be used to higher order elements by subdividing the element into triangular sub-elements.Due to singularity,the semi-analytical integral regularization algorithm is applied to the integral element close to the source point.The conventional Gauss quadrature is kept in the integral element far away from the inner point.The potentials and fluxes at the interior points close to the boundary are computed for three-dimensional heat conduction examples.The results demonstrate the accuracy and effectiveness of the algorithm.

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A Rational Interpolation for Temperature Distribution in Convex Domains WANG Zhao-qing, FENG Wei 2005, 22(6): 37-44.  Abstract ( )   PDF (658KB) ( )   Using geometric method,a rational interpolation within convex polygons is constructed and extended to include side nodes.The computational expressions of rational shape functions are shown.Different from Wachspress' rational interpolation,the interpolations presented in this paper include no undetermined constant.A convex domain is approached by a convex polygon,and the approximated temperature distribution within the domain can be interpolated with the temperature data at the boundaries of the domain.The interpolated distribution of temperature within disc and square domains is calculated.

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Automatic Control of Time Step in Two-dimensional Three-temperature Hydrodynamic Calculations FU Shang-wu, DAI Zi-huan, WU Ji-ming 2005, 22(6): 45-49.  Abstract ( )   PDF (337KB) ( )   The time step control in two-dimensional three-temperature hydrodynamic calculations is studied.Based on numerical stability and accuracy we propose several conditions that restrict the time step.These conditions change the time step automatically in computation so that the calculation proceeds with the most economical and reasonable time step.Numerical results are shown to demonstrate the efficiency of the method.

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Collision of Discontinuities in a Conservative Front-Tracking Method LIU Yan, MAO De-kang 2005, 22(6): 50-56.  Abstract ( )   PDF (401KB) ( )   Techniques to treat interaction of tracked discontinuities,such as "stack",in a one-dimensional front-tracking method based on conservation (conservative front-tracking method) are developed and described in details.A numerical example is presented to illustrate the efficiency of the techniques.

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A Stratified Sample Method of Scattering Source for Time-dependent Monte Carlo Transport DENG Li, ZHANG Wen-yong, HUANG Zheng-feng, WANG Rui-hong, XU Hai-yan, LI Shu 2005, 22(6): 57-63.  Abstract ( )   PDF (323KB) ( )   A parallel algorithm for time-independent Monte Carlo transport is successful since particles are independent and they are distributed to multiple processors.However,for time-dependent Monte Carlo transport problems, the parallel efficiency reduces and the parallel scale is limited due to the communication of scattering source attribute and meshes in each time-step.We propose two algorithms in them adaptive processor assignment and optimized processor choice are obtained.With a Monte Carlo stratified sampling technique for scattering source treatment the communication cost is reduced greatly.The parallel expandability is improved.A large speedup over the basic algorithm is obtained.

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A Fast Fourier Transformation Micromagnetism Method ZHONG Ke-hua, FENG Qian, WENG Zhen-zhen, HUANG Zhi-gao 2005, 22(6): 64-68.  Abstract ( )   PDF (272KB) ( )   A calculation method based on fast Fourier transformation and micromagnetism (FFTM) is presented.It is applied to the numerical calculation of two-dimensional nanomagnetic systems.Numerical calculations show that the results of FFTM method are similar to those of the method in which the dipole-dipole interaction is performed straightforward with truncation.The precision and the speed of calculation are improved.It is shown that the FFTM method provides a fast and efficient way for magnetic systems with long-range dipole-dipole interaction.

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A Wavelet Interpolation Galerkin Algorithm for Static Electromagnetic Field Analysis in Irregular Regions HOU Xia, FAN Zhi-hua, GU Yong-geng, YANG Hong-bo 2005, 22(6): 69-78.  Abstract ( )   PDF (477KB) ( )   A Wavelet Interpolating Galerkin Method (WIGM) for elliptic partial differential equations,especially in irregular regions,is considered.It is proved that the WIGM produces an approximation with an error no more than C2-m in the Sobolev space norm.A numerical WIGM algorithm for static electromagnetic field analysis in irregular regions is presented.A symmetric interpolating scaling function is selected as the base function.Its symmetry and relation with average-interpolating scaling function are used to reduce numerical computations.Examples presented demonstrate validity of the algorithm.

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Computation of Two Dimensional Unstable Manifolds LI Qing-du, YANG Xiao-song 2005, 22(6): 79-84.  Abstract ( )   PDF (391KB) ( )   A practical and efficient computation method for stable and unstable manifolds is proposed.Pictures of unstable (stable) manifolds are obtained easily.Thus one can investigate geometrically dynamics of a dynamical system and features of stability regions.The algorithm consists of two steps:Firstly,calculate on well distributed points in the unstable manifold by means of integration so that details of the unstable manifold are shown.Secondly,draw a picture of the manifold with these points by means of triangle partition.

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Frequency Drift Rate of Solar Radio Fiber Structures ZHANG Wen-juan, WANG Shu-juan, SONG Guo-xiang, YAN Yi-hua 2005, 22(6): 85-89.  Abstract ( )   PDF (407KB) ( )   The fiber fine structure in solar radio bursts carries small-scale magnetic field information in the initial phase of the burst.We deal with fiber structures to analyze the frequency drift rate.The background is obtained by a wavelet transformation.With a subtraction of the background and a threshold processing,the fiber structures are seperated.We select continuous segments in each channel.The cubic spline interpolation is used to fit the intensity-time relation with which the moments of intensity maxima are determined.Finally,the drift rate is calculated with linear regression.The algorithm is used to calculate frequency drift rate of the radio fiber event on 21-April-2002.The mean frequency drift rate obtained is beween -0.041 0~-0.013 8 GHz·s-1.

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A Quadrature Method and its Splitting Extraplation for Mixed Boundary Integral Equations of Stable Problems HUANG Jin, ZHANG Qian-chuan, LU Tao 2005, 22(6): 90-94.  Abstract ( )   PDF (218KB) ( )   We present a quadrature method for mixed boundary integral equations of stable problems,which provides high accuracy and less complexity.Discrete equations are solved in parallel according to the coarse mesh partitions.Approximations with high accuracy are obtained by splitting extrapolation methods based on multivariate asymptotic expansion of errors.Besides,a posteriori asymptotic error estimate is derived.