数值方法

In this paper, we consider the following computing method of tridiagonal matrix:(1) decoupling of linear equation;(2) determination of determinant and eigenvalue-eigenvector relation;(3) matrix inversion.

二引宫在数值计算中，有许多问题足后归结为三对角矩阵的计算涸此研究它们的计算方法是有意义的。此外，有些三对角阵的计算方法可以做为带状阵计算的借鉴。

Measuring some turnery and grinding work pieces from the scene,we can get the good result that can explain this measuring diameter instrument has low price.And its measure method is simple,numerical value intuitional and accurate.Under the available school condition,it can self control,process,adju...

其实验效果良好，并说明，仪器价值低，测量方法简便，数值直观而准确，可以利用学校现有条件，自制加工调试和应用，从而改进了以前的测量手段和方法，提高了测量精度和实验教学的质量。

In this paper, we firstly make some qualitative analysis to Lorenz critical chaotic system, and then lead it to the corresponding unstable equilibrium point and periodic orbits in terms of the linear state feedback approach. Then we make a lot of simulations which indicate this method to be feasible. Fractional-order system, as well as Lyapunov exponent, has been used as a powerful tool for the quantitative study of chaotic systems.

本文首先对Lorenz临界混沌系统进行基本定性分析，然后利用线性状态反馈方法将其制到相应的不稳定的平衡点与周期轨道上来，并证明了被控制的Lorenz临界系统是全局渐进稳定的，并对取得的结果作了大量的数值模拟，模拟结果证实该控制方法简单有效可行。

A conservative form for the flow equation is established by using upwind finite volume element method.

考察非饱和水流问题的模型方程，利用线性迎风有限体积元方法建立非饱和流动的守恒形式，并获得该方法形式为O的误差估计，最后给出数值模拟。

For the first patern, elastic dynamics is adopted to study the steady state rolling contact, elastic dynamics incorporating with rigid dynamics is adopted to study the non-steady state. For the steady state, the analytical solution is obtained, and for the non-steady state, the variational formulation to solve the problem numerically is derived For the later patern, the function type friction coefficient is introduced. On the basis of the quasi-stastic theories of constant friction coefficients, both the exact theory and the simplified theory of the function type friction coefficient are established, the computer programms for both the theories are also made out. Using the function type friction coefficient, Shen-Hedrick-Elkins theory's application range is extended to large creepage .

对于速度对接触体力学特性的影响，本文采用弹性动力学方法和弹性动力学与刚体动力学相结合的方法分别对稳态和非稳态两种情况进行了研究，得到了稳态情况的解析解，给出了对非稳态情况进行数值求解的变分公式；对于速度对相关物理量的影响，本文主要讨论了速度对摩擦系数的影响，在滚动接触准静态理论的基础上引进了函数型摩擦系数，建立了函数型摩擦系数的滚动接触准静态精确理论和简化理论，并分别编制了相关的计算程序，还用函数型摩擦系数将简便的Shen-Hedrick-Elkins理论的适用范围扩展到大蠕滑区。

The long-term seepage control effects of the surrounding rocks of the underground powerhouse are performed by a stationary seepage analysis method combining the variational inequality formulation of Signorini's type with an adaptive penalty Heaviside function to guarantee the numerical stability and convergence. Meanwhile, the difficulty in finite element mesh generation is reduced and the calculation time and modeling accuracy are balanced with a global model of equivalent modeling and a submodel of accurate modeling for drainage hole array.

为确保数值计算的稳定性和收敛性，采用Signorini型变分不等式和自适应罚函数相结合的稳定渗流分析方法，对厂房围岩的长期渗控效应进行计算分析；同时，采用基于等效模拟的整体模型分析和基于精细模拟的子模型分析相结合的方法，以减小有限元建模难度并协调计算量和计算精度之间的矛盾。

The numerical method of the variational principle combined with finite element method is presented in the paper.

文中介绍了运用该变分原理并结合有限元方法进行数值计算的方法。

In the fourth chapter, using the magnetic vector potential as the unknown variable, a mathematical model for numerical calculation of the magnetic field and loss distribution in 3-phase 5-limb transformer core is presented.

第三章针对变压器铁心结构的特点，对各向异性非线性边值问题的有限元分析方法进行了详细的阐述，并推导出了实用的N-R格式及单元分析格式，对具有多媒质单元的有限元分析方法进行了介绍，为变压器铁心磁场及损耗分布的数值计算奠定了基础。

In order to analyze the stiffness of 3D 4 directional braided composites, the homogenization theory based on the multi-scale perturbation theory was used as the basic theory. The virtual displacement principle was used to educe the homogenization formulation of effective elastic modulus and the schemes to solve the problem using finite element method. The effective elastic modulus of 3D braided composites were predicted by this method and the calculation results agree quite well with experiment results.

在对三维编织复合材料刚度性能的分析过程中，以基于小参数渐近展开和多尺度摄动方法的均匀化理论为理论基础，用虚位移原理导出了等效弹性模量的均匀化列式及其有限元求解方程，从而通过细观和宏观有限元的数值分析方法预测了三维四向编织复合材料的等效弹性模量，预测结果与实验结果较为吻合。

The characteristics of a new kind of linear phase retrieval wavefront measuring method were analyzed.

利用数值仿真方法对一种基于线性相位反演波前测量方法的性能进行了详细分析。

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。