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AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS

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Journal of computational mathematics 2003年第2期21卷 125-134页

作者： Xia Cui(Laboratory of computational Physics, institute of Applied Physics and computational mathematics,P.O. Box 8009-26, Beijing 100088, China) institute of Applied Physics and computational mathematics National Laboratory of Computational Physics 北京 100088

AD (Alternating direction) Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal H1 and L2 convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

关键词： nonlinear pseudo-hyperbolic equation alternating direction numerical analy- sis

An Explicit Exact Solution of a Nonlinear Schrödinger Equation for Short Ultraintense Laser Pulse in an Underdense Plasma

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Chinese Physics Letters 1996年第8期13卷 561-564页

作者： GAO Hong-jun Laboratory of computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088

A nonlinear Schrödinger equation for short ultraintense laser pulses in an underdense plasma has been discussed,and three types explicit exact solutions of this equation are obtained by using analytical method.

关键词： method intense equation

PARAMETER IDENTIFICATION IN FRACTIONAL DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2013年第3期33卷 855-864页

作者：李景郭柏灵 School of mathematics and computational Science Changsha University of Science and Technology institute of Applied Physics and computational mathematics

This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determination of the fractional derivative order and the dif- fusion coefficient p（x） by fo u（0, s）ds, 0 〈 t 〈 T for one-dimensional fractional diffusion-wave equations. Besides, if 0 〈 α 〈 1, we show the unique determination of the source term f（x, y） by U（0, 0, t）, 0 〈 t 〈 T for two-dimensional fractional diffusion equations. Here, a denotes the fractional derivative order over t.

关键词： Fractional differential equation inverse problems parameter identification

The Quasi-reversibility Method to Solve the Cauchy Problems for Parabolic Equations

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1617-1628页

作者： Jing LI Bo Ling GUO School of mathematics and computational Science Changsha University of Science and Technology institute of Applied Physics and computational mathematics

In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.

关键词： Ⅲ-posed problems parabolic equations Cauchy problems quasi-reversibility

Numerical Study on the Whole Process of Fireball Evolution in Strong Explosion

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Communications in Theoretical Physics 2019年第11期71卷 1388-1392页

作者： Yin Xia Chuang Xue Chen-Guang Li Guang-Wei Meng Ying-Kui Zhao Jun Yan Bai-Wen Li institute of Applied Physics and computational mathematics

With the actual mean free path for radiation in air and a simplified nuclear device, a one-dimension simulation research on fireball phenomenon in a sea level atmosphere is carried out based on the multi-group radiation hydrodynamic codes(RDMG). It is shown that our theoretical calculations can describe the whole process of the fireball evolution for strong explosions from the early X-ray expansion stage to the shock wave propagation stage. The radius of the shock wave and the brightness of the fireball are in good agreement with the experimental results. The whole thermal radiation power curve of the fireball evolution for strong atmospheric explosion at sea level is plotted for the first time. The impact of radiation opacity of the nuclear device material on the early fireball phenomenon is also studied. It is found that trajectories of the radiation fronts and case shocks change with the opacity of equivalent device *** our simulations, we find that only the early fireball depends on the details of the nuclear device, and after the formation of main shock, the evolution is determined by the properties of hot air for strong atmospheric explosion.

关键词： fireball phenomenon radiation transfer equation the shock wave brightness

Monte Carlo simulation and parameterized treatment on the effect of nuclear elastic scattering in high-energy proton radiography

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Chinese Physics C 2015年第7期39卷 97-101页

作者：许海波郑娜 institute of Applied Physics and computational mathematics

A version of Geant4 has been developed to treat high-energy proton radiography. This article presents the results of calculations simulating the effects of nuclear elastic scattering for various test step wedges. Comparisons with experimental data are also presented. The traditional expressions of the transmission should be correct if the angle distribution of the scattering is Gaussian multiple Coulomb scattering. The mean free path（which depends on the collimator angle） and the radiation length are treated as empirical parameters, according to transmission as a function of thickness obtained by simulations. The results can be used in density reconstruction, which depends on the transmission expressions.

关键词： proton radiography multiple Coulomb scattering angle collimator nuclear elastic scattering Geant4

Transmission calculation by empirical numerical model and Monte Carlo simulation in high energy proton radiography of thick objects

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Chinese Physics C 2015年第10期39卷 127-130页

作者：郑娜许海波 institute of Applied Physics and computational mathematics

An empirical numerical model that includes nuclear absorption, multiple Coulomb scattering and energy loss is presented for the calculation of transmission through thick objects in high energy proton radiography. In this numerical model the angular distributions are treated as Gaussians in the laboratory frame. A Monte Carlo program based on the Geant4 toolkit was developed and used for high energy proton radiography experiment simulations and verification of the empirical numerical model. The two models are used to calculate the transmission fraction of carbon and lead step-wedges in proton radiography at 24 GeV/c, and to calculate radial transmission of the French Test Object in proton radiography at 24 GeV/c with different angular cuts. It is shown that the results of the two models agree with each other, and an analysis of the slight differences is given.

关键词： proton radiography angular distributions scattering Gaussians Geant4 transmission

Monte Carlo fission matrix acceleration method with adaptive mesh

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Nuclear Science and Techniques 2015年第5期26卷 118-122,F0003页

作者：潘流俊王瑞宏江松 institute of Applied Physics and computational mathematics of Beijing

In large-scale, loosely coupled systems, Monte Carlo criticality calculation always suffers from slow fission source convergence resulting from the high dominance ratio. The fission matrix acceleration method has shown its potential to accelerate the convergence of the fission source in many numerical simulations. In practice,however, instability of this method may be caused by imbalanced precisions of elements of the fission ***, an improved method, in which the space mesh used to compute the fission matrix is defined adaptively based on the fission bank in each cycle, is introduced. The proposed method ensures balanced precisions of elements of the fission matrix, so is more stable than the existing fission matrix method.

关键词：裂变元素矩阵元素蒙特卡罗自适应网格加速方法临界计算平衡精度松散耦合

A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS

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Acta Mathematica Scientia 2010年第6期30卷 1851-1864页

作者：江松欧耀彬 LCP Institute of Applied Physics and Computational Mathematics

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.

关键词： blow-up criteria strong solutions compressible Navier-Stokes equations heat-conductive flows