迭代计算

The Schur subspace iteration method is applied for the dynamic characteristic analysis of damped structure vibration system and coupled fluid－structure system. This method avoids complex computation and has good numerical stability. A accelerated technique and a pre－process method for the system matrix are suggested to improve the computational efficiency. The generalized uncoupled equation is obtained from the Schur matrix and a back substitution scheme of response computaton is developed.

第三部分将非对称特征值问题的Schur子空间迭代法应用于非经典阻尼结构振动系统和流固耦合系统的特征值分析，建立了相应的具体算法，并给出了用以提高迭代收敛速度的迭代加速和矩阵预处理等实用技术；利用Schur矩阵的结构特点，推导了系统方程的动力解耦形式，给出了响应计算的回代求解格式。

Based on decomposition-coordination model of an electric power system,the general augmented Lagrange method and auxiliary problem principle are adopted to form iterative distributed transfer capability computation framework,in which the influence on the internal system exposed by external system is considered through exchanging the information of boun.

该方法通过分解-协调模型实现互联电网的解耦，采用增广拉格朗日法和辅助问题原理实现输电能力按地理分区，形成一个迭代形式的分布式输电能力计算框架，迭代中通过交换边界节点信息将互联外网信息反映到各分区的计算中，各地的子网络计算相对独立。

Chapter 4 puts up the basic theory of non-linear finite element calculation methods and deduces calculation iterative formula and relevant accelerating iterative format. In the calculation of non-linear finite element, yielding element calculation is a difficult problem,"fictitious elastic stress" methods propounded in this paper puts the axe in the helve.

第四章提出了非线性随机有限元法的基本理论，并推导了计算迭代公式，为加快计算速度，提出了相应的加速迭代格式，对于基于非线性随机有限元的可靠度计算中，屈服单元的计算方法是一个难题，本文提出了"虚拟弹性应力"法，较好的解决这个难点。

Aimed at the calculation complexity of Newton iterative method for solving nonlinear equation,a new iterative method with higher convergence rate and without derivative calculation is presented in this paper.Its convergence rate p is 1.839 and it doesn't need to calculate derivative.

为解决Newton迭代法求非线性方程数值解时必须提供一阶导数值的问题，提出了一个新的迭代方法，该方法不需提供导数值而只需计算函数值，且具有p=1.839的收敛阶，因而是一个收敛速度快且不需要计算导数值的迭代方法。

By using K-ε twoequation model to modify turbulent flow, the simulation results could coincide better with the real filling processes. Combined flow path analytical program which was used to revise the ingate velocity, it increased the accuracy effectively, and raised the calculating velocity.

该软件首次采用非均匀网格剖分技术，更为逼真地反映了铸件的几何形状；耦合计算过程中，采用简化耦合算法，避免了繁复的迭代过程，缩短了迭代时间，且计算精度能满足工程要求；采用K-ε双方程紊流模型对紊流流动进行修正，模拟结果更加符合实际充型过程；联合流路解析程序修正内浇口入流速度，有效地提高了计算精度，加快了计算速度。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的"半收敛"性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

In this paper, the generator model of constant transient voltage and the invariableness impedance model was used, and the saliency of generator is included; through the analysis of the characteristic of the network equation calculation in the transient stability analysis, a new node ordering algorithm is proposed. Better initial value can accelerate the convergence rate of the networking equations, reduce the number of iterations, thus to cut down the amount of calculating time.

本文首先建立了适合于暂态稳定分析的简单模型，其中发电机采用E_q恒定模型，考虑了发电机的暂态凸极效应，负荷采用恒定阻抗模型；研究了电力系统的暂态稳定分析方法，指出目前数值积分暂态稳定计算方法中存在的不足，主要是网络方程的求解速度过慢；分析了暂态稳定计算中网络方程的特点，将稀疏技术应用于网络方程的求解，提出了一种新的节点编号方法——最小度最小有源节点道路集算法，减少了网络方程的计算量；在进行交替迭代求解时，将预测算法应用于每一积分步网络方程功角和电压的初值估计当中，应用自回归算法和广义延拓算法，期望给出一个更有效的电压和功角初值方案，来加快方程的收敛过程，减少方程迭代的次数，以提高计算速度。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的&半收敛&性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

For non-intense beams,particle trajectory can be obtained by multiplying linear transport matrices. For nonlinear transport of intense beams,the influence of space-charge effect on beam transport needs to be taken into account,and self-consistent solution should be derived because of the interaction between charged particle distribution and space charge field. In the program,components and currents are divided into equal intervals,respectively,and each interval is treated as a uniform solenoid field.

程序在计算非强流脉冲束流的线性传输时，粒子的轨迹通过矩阵的直接相乘计算得出；程序在计算强流脉冲束流的非线性传输时，需要考虑束流中的空间电荷效应对束流传输的影响，在束流运动过程中，空间电荷场也在不断地变化，而且粒子运动的轨迹与空间电荷势又是相互依赖的，因此需要求得一个自洽的解，先把元件分成若干均等的区间，把电流分成若干等份，后采用束流电流迭代与元件区间迭代的计算方法。

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。