求解

The solver is used to investigate laminar and turbulent separated flows around a 6:1 prolate spheroid at high incidence angles and their effects on hydrodynamic forces. The second separation flows are successfully identified in both laminar and turbulent flow simulations. The computations are shown to agree well with available experimental and numerical data and the physics of 3D large-scale flow separations and vortex shedding are confirmed.

应用所开发的求解器，以6：1长椭球体为算例计算了回转体在大攻角下定常斜航运动时的三维粘性流场及水动力，对层流流动和湍流流动分别进行了计算，分析了层流与湍流分离流动和涡旋产生的特点及其对水动力的影响；计算结果与他人的试验和计算数据比较，吻合程度良好，表明应用本求解器能够正确模拟这种以层流/湍流分离流为主的复杂粘性流动，得到相当精确的水动力，检验和验证了该求解器精确模拟回转体在大攻角下的粘性分离流动和计算水动力的能力。

The hierarchical structure system was calculated by means of fuzzy comprehensive evaluation theory to realize quantification of the evaluation result. Subequently, based on the solution idea of multi-object reverse problem, a method for particular solution for big/small benchmark was derived, and then a set of virtual decision making units (DMU0) was solved.

利用模糊综合评价的理论对多层结构的系统进行评价计算，实现了评价结果量化；同时，基于模糊多目标决策反问题的求解思路，推导了求解大小标杆量化特解的方法，并以此求解出一组虚拟决策单元(DMU0)。

The traditional methods of solving Rational Function Model is not stable.

基于控制点数据的有理函数模型由于求解稳定性差、精度浮动大，目前还没有一个成熟的算法模块的软件集成，针对这些问题，本文从数学的角度分析造成有理函数模型求解不稳定的各项因素，寻找一种相对稳定的求解算法。

By introducing a new concept-Motion Characteristic Transformation Matrix , this thesis presents a top-down solving method to decompose the complex requirement into several simpler ones by sophisticated matrix operation, row and column shifting and velocity character expanding strategy.

作者提出运动特性变换矩阵，将运动类型、运动轴线以及速度特性等三个运动求解过程中所需的运动特性有机地集成于一体，并通过矩阵的行列变换以及基于规则的速度特性扩展策略，将复杂运动需求分解为简单的运动需求后进行求解，从而实现了自顶向下的复杂运动需求的求解。

A 3rd-Runge-Kutta-5th-WENO scheme is used in this study to get solution of the Level Set advection equation. A Projection method is used to solve the N-S equation, and different discretization schemes are presented. A TDMA algorithm is used to solve the energy equation. With the use of these methods, a numerical simulation of vapor-liquid two-phase flows during condensation with large density ratio has been successfully realized.

本文应用三阶Runge-Kutta－五阶WENO组合格式求解Level Set输运方程，应用投影法求解气－液两相流流场N-S方程，给出了不同投影法的具体格式，应用TDMA算法求解气－液两相流场的能量方程，成功实现了对大密度比气－液两相流冷凝流动问题的数值模拟。

With the development of science and project technology, more and more questions need the solution of big linear systems. This solution is one of the fastest ways for researching numerical algebra, especially for the big sparse matrix.

随着科学和工程技术的发展，越来越多的问题需要求解大规模的线性方程组，对这类方程的快速求解已成为数值代数研究的热点之一，特别是具有稀疏结构的大型方程组的求解。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

To solve it, we turn it into nonsmooth equations, utilizing inexact theory we give an inexact generalized Newtons method and under some mild conditions we prove that it is global convergence and superlinear convergence .

首先将其约束问题的求解转化为非光滑方程组的求解，然后利用不完全求解理论给出了一个非精确的广义牛顿算法，在一定的条件下证明了算法的全局收敛性和局部超线性收敛性并给出了LC~1非线性约束问题的收敛性条件。

In order to overcome the shortcoming brought from the calculation of the trigonometric function, the approach of numerical equivalent, which remove the trigonometric function from the nonlinear equations of SHEPWM, is presented in this dissertation.

在特定消谐方程组中含有大量的三角函数，方程求解时，大量的三角函数计算限制方程求解速度的同时也降低了求解精度。

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。