变分法

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Structural analysis; state-space method; variation principle; computer simulation; engineering application

结构分析；状态空间法；变分原理；计算机仿真；工程应用

Based on the Hamiltons principle and the displacement variation principle, one-dimensional discrete finite element method is developed for vibration analysis of thin-walled members.

对于动力分析部分，概述了Hamilton原理，并由位移变分原理出发推导出考虑剪力滞效应的薄壁杆件振动的一维离散有限元法。

The approximation of meshless methods, the selection of weight function, the variational form and the discrete equation, and the numerical implementation are described.

描述了无网格法的近似方案、权函数的选择、变分形式和离散方程以及数值求解的实现。

Using the variational formulation and its discretization equation, we get its finite element algebra equation and solve it by the method of Newton iteration.

通过对方程做变分、离散得到其有限元代数方程组，并选择了Newton迭代法来求解该方程组。

The present variational formulation will be used to achieve a novel semi-analytical formulation for more complex piezoelectric material problems in engineering applications.

本文的变分公式将用来构造新颖的适应工程领域复杂压电材料问题的半解析法。

Moreover,the weighted residual method is utilized forestablishing the generalized variational formulation for solving three-dimensional eddy-current problems.

此外，介绍了用加权余量法建立三维涡流问题的等价广义变分问题的基本方法。

Based on the Galerkin Method the variational problem for the point source 2.5-dimensional electricfield is derived and the corresponding finite element equations are obtained.

基于Galerkin法推导了点源2.5维电场的变分问题，得到了对应的有限元方程组。

In order to clearly recognize the geophysical response of carbonate reservoir,based on preliminary recognition of Ordovician carbonate reservoir under the basal surface in Tahe oilfield,some regular vug models and random arranged vug models were designed and built. The variable-grid finite difference method was used to simulate the seismic wave propagation in these models. Then,the seismic records of the models were analyzed and the effect to seismic reflections caused by vug is studied. The impact rule of regular vug scale and random arranged vug density on seismic attributes was obtained.

为了研究碳酸盐岩储层的地球物理响应特征，在对塔河油田奥陶系风化面下碳酸盐岩储层初步认识的基础上，利用随机介质建模技术，设计并建立了一系列碳酸盐岩储层规则孔洞和随机孔洞模型，并应用变网格有限差分法对地震波在孔洞模型中的传播进行了正演计算，对模拟得到的地震属性进行了分析，研究了孔洞对地震反射特征的影响，获得了规则孔洞尺度以及随机排列孔洞密度对地震属性的影响规律。

Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger_Reissner variational principle.

从Hellinger_Reissner变分原理出发，在柱坐标系中，导出圆柱壳的弱形式混合状态方程和边界条件，联用状态空间法给出叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。

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。