变分法

To one kind of variational inequalities, some researchers give an alternating direction method, which solve a linear variational inequality and a system of nonlinear equations in each iteration.

针对一类变分不等式，有研究者给出了一种交替方向法，在每一步迭代中分别要求解一个线性变分不等式和一个非线性方程。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

In using the FDTD method to research the transient process of the overhead line, for the convenience of the time domain convolution, the Vector Fitting method is adopted to expend the frequency domain form of ground return impedance into a sum of finite exponential functions which are easy to be treated and test to be valid.

提出了应用矢量匹配法逼近传输线频变阻抗的时域处理方法，从而解决了时域有限差分法难以处理频变问题的困难。

The equations of a high-speed rotating plate are obtained using Jourdain＇s velocity variation principle and the finite element method and MTA are used for discretization.

基于Jourdain速度变分原理，先推导出做高速旋转薄板的动力学连续变分方程，再用有限元法对柔性薄板进行离散。

And the conservation laws of moment and momentum are obtained by the combining the tiny element analysis method in continua mechanics with variation principle in analytical mechanics.

论文摘要：本文在建立时变边界挠性体的动力学方程时，将并入的质量对挠性体的作用当作时变边界上的表面力，并将连续介质力学中的微元分析法和分析力学中的变分原理相结合，导出了时变边界的变质量刚体的动量和动量矩矩方程。

This section further presents three kinds of computation schemes, which are discretization schemes based on linear interpolation, locally quadratic interpolation and mixed quadratic and cubic interpolation.

吴微在[21]中使用三角剖分及外心对偶剖分给出了解双调和方程的基于Ciarlet-Raviart变分原理的混合广义差分法，理论分析部分采用了[26]中的有关思想。

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

In this paper,a two dimension variation method is applied to compute tensile fracture surface fractal dimensions of a grain composite material LDPE/CaCO 3,and set the relationship of tensile fracture surface fractal dimensions and tensile ultimate stress and material filler weight content percent .

应用计算断口表面分形维数的二维变差法，计算了颗粒复合材料LDPE／CaCO3拉伸断口的分形维数，并且建立了断口分形维数与强度极限和填料颗粒含量之间的关系。

Based on variational principle and split-based interpolation finite element method for fast and accurate analysis of normal mode helical antenna,Combination of genetic algorithm and then load the normal mode helical antenna loaded on the value of lumped elements,Load location,and matching network integrated optimal design parameters,And using Sherman-morrisorr Woodbury formula to quickly solce the load component values and load the changed position of the impedance matrix equation to improve the efficiency of optimized design.

采用基于变分原理和剖分插值为基础的有限元法来快速精确分析法向模螺旋天线，然后结合遗传算法对加载法向模螺旋天线上的加载集总元件的值、加载位置以及匹配网络参数进行一体化优化设计，并采用Sherman-Morrisorr Woodbury公式来快速求解加载元件值和加载位置改变后的阻抗矩阵方程，提高优化设计的效率。

We mainly discuss three types of inpainting models: the Bayesian model, geometric models and PDE models with emphasis on investigating TV inpainting, elastica inpainting and Mumford- Shah inpainting of PDE models. After studying the level set method and its applications to image processing, we concentrate on discussing the inpainting model...

在介绍水平集法及其在图像处理方面的应用之后，进一步深入地讨论了一类图像修复的变分模型—Mumford-Shah-Euler模型，在此基础上利用水平集法，提出MSE模型的数值逼近的算法格式，并对一些具体的图像修复问题开展数值模拟和修复，深入分析了MSE模型及水平集法在图像修复中的优缺点，这些结果在理论和实际应用中都很有意义。

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。