数值的

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

For example, in the design of antenna, it is always involve the imaginaries Bessel function, so these work are belonged to the base research work, but it is important.

本文对各向异性介质偶极天线辐射场的数值计算的研究以及各向异性介质波参数的数值计算的研究目前还没有文献系统介绍，但这些内容对进一步研究探地雷达辐射场的规律是必不可少的，尤其是传播常数，它在探地雷达的研究中仍然是一个非常重要的公式，对其的深入研究有利于对探地雷达资料的正确解释。

The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables.

该方法具有只进行一次随机温度场分析便可以获得其响应的数字特征的优点。3、温度场的非概率凸集合理论模型的摄动数值解法将结构导热的物理参数、温度场的初始和边界条件等不确定性参数以凸模型加以描述，基于矩阵摄动理论和处理不确定问题的凸集合理论模型的结合，导出有界不确定参数瞬态温度场响应所在集合的上、下界摄动计算公式。4、具有区间参数的瞬态温度场数值分析考虑结构瞬态热传导问题的不确定性，将结构各物理参数和温度的初、边值条件均视为区间变量。

Meanwhile, it could be seen that there does not exist a confidence interval with width less than 0.5 because of the property of Poisson distribution. Based on these conditions, the author mainly carried out research into two aspects of this problem as follows. Firstly, by numerical and theoretical analysis, the author compares some existent confidence intervals, for example,"exact" confidence interval, Wald confidence interval and Bayesian confidence interval, and finds some deficiencies points of the confidence intervals, whose modification version has been proposed .Also, several better confidence intervals such asare also presented .Secondly, for given confidence coefficient and interval width, the author constructs a class of asymptotical two-stage interval estimate procedures. At the same time, under varies restriction of confidence coefflcientent interval width, the optional sample size of the first stage has been computed by numerical computation. The numerical computation shows that the method considered in this dissertation have good properties and applied value.

同时，由于Poisson分布的特性，我们知道不存在其参数区间长度小于0.5的置信区间，基于这些情况，我们主要展开了以下两个方面的研究：一是利用数值计算分析与理论分析的方法对现有的若干置信区间如"精确"置信区间，Wald置信区间，Bayes置信区间等进行分析比较，发现了一些缺陷，针对这些缺陷，我们进行适当的修正，并得到几种性质较好的置信区间如：修正大样本区间Jeffreys原则下置信区间二是针对已给定的置信系数与区间长度，我们提出了一种渐近的两阶段区间估计程序，并利用数值计算的方法，在各种置信系数与区间长度限定下，算出了最优的第一阶段观测次数，大量数据表明，本文考虑的方法性态良好，具有应用价值。

He proved that the left ward turning of Yangtze river diluted water is mainly resulted from the interaction between the bottom declining and the lag of the transversal pressure gradient, made the numerical simulation and preliminary study on the thermohaline staircase structure formation mechanism, improved American Academician Wunsch's inverse method of ocean circulation, jointed the discover of " Mindanao Under Current", which is the first ocean current found and named by Chinese scientists and widely accepted over the world, simulated the horizontal and vertical carbon fluxes in East China Sea by a simple ecosystem model, estimated the photosynthesis efficiency less than 8% in Jiaozhou Bay, applied statistical downscaling technology to Chinese coast and Japanese islands realizing the simulation and forecast of sea level low frequency variations, pointed out that the quasi-periodicity of El Nino events should be resulted from the interaction between the 3~4 year oscillation in tropical Pacific and decadal oscillation in the northern Pacific of middle latitudes of the air-sea coupled climate system and at decadal time scale the precipitation influence on sea level variation along Chinese coast and Japanese islands becomes more important, which is closely related to the decadal oscillation of air-sea coupled climate system, therefore precipitation most likely play a major role for the decadal oscillation formation;; proposed Extended Associate Pattern Analysis to analyse combined observed datasets of sea surface temperature and sea level pressure or geopotential hight at 1000 hPa (GH1000) over the Pacific and related seas.

论证了长江冲淡水向左转向主要由于底形下倾与横向压力梯度滞后相互作用的结果。对温盐阶梯结构的形成过程及物理机制进行了数值模拟与初步探讨。改进了美国科学院院士Wunsch的大洋环流反演法。与胡敦欣院士共同发现了"棉兰老潜流"，这是第一支由中国科学家发现、命名并得到普遍承认的洋流。借助较为简单的生态模式数值模拟了东海的水平与垂直碳通量；胶州湾浮游植物的屏蔽效应可以使底层海水温度在升温季节降低2度，由此推算出其光合作用的效率应小于8%；浮游植物春季水华的生物过程实际上强化了海水层化的物理过程。将统计学降尺度技术应用于日本列岛和我国沿海，实现了海平面长周期变化的模拟与预报。

This paper introduces the food refrigerated theory and the basis of the current industry refrigerated developments in the situation; And then in the long cylindrical-shaped food heat conduction process and the mathematical model using the method of differential thermal conduction equations for discrete, Programming come through long cylindrical-shaped food cooling process numerical solution; After further analysis of numerical solution of the test results; Finally, the impact of the cooling process food all relevant factors, such as moisture content, wind speed and temperature of the cooling medium for in-depth research, while comparing the different shapes of food to food cooling process.

本文首先介绍了有关食品冷冻冷藏的基础理论和目前冷冻冷藏行业的发展的发展概况；然后研究了长圆柱状食品热传导过程的数学模型并利用差分的方法对热传导方程进行离散，通过编程得出长圆柱状食品冷却过程的数值解；之后再分析解对数值解的结果进行验证；最后对影响食品冷却过程的各相关因素，如含水率、风速和冷却介质温度等进行了深入的研究，同时又对比了不同形状的食品对食品冷却过程的影响。

Based on the theory of large eddy simulation and the method of VOF , the initial breakup process of fuel liquid jet, which eject from the nozzle exit at the time scale of micro-second level, is investigated. The mechanism of primary atomization is analyzed, and the initial breakup model of liquid jet is presented. By modeling and numerical simulation of atomization for a diesel nozzle under the given conditions, the initial umbrella-like spray shapes are obtained, which fits better with the experimental results. Meanwhile, the droplets secondary breakup process, such as leeward RT breakup, dumbbell-like breakup and droplets coalescence, etc. are exhibited visually.

基于大涡模拟LES理论和VOF方法，考察了燃油喷雾初始时刻即时间尺度为微秒级的液柱破碎过程，分析了初始破碎的机理，给出了该时间尺度下液柱初始破碎过程的模型；通过对一特定条件下的柴油机喷油器的建模和喷雾过程的大涡数值模拟，获得了液柱初始时刻"伞状头部"的喷雾形态，所得计算结果与相应的试验数据符合较好；数值模拟还直观地展现了液滴背风RT破碎、哑铃型破碎以及液滴的聚集融合等液滴的二次雾化过程。

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

Firstly,the differential equation with parameters is given,at the same time,in order to let the truncation error of differential equation reach O(Δt~2+Δx~4) as high as possible,the method of undetermined coefficent is used to appropriately select the expression of these parameters.Secondly,the stability condition of the scheme derived is given by using the Fourier method of stability analysi...

首先给出了含参变量的差分方程，并用待定系数法适当地选取了这些参数的表示式，以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4)；其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件；然后给出了确定差分格式中参数的两种方法，得到了一个稳定性条件为r/3的分支稳定的高精度显式差分格式；最后给出了数值例子，数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性。

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。