变分方程组

Its major feature is to reduce EMS memory allocation greatly by the help of two one dimensional arrays: one is used to deposite the elements within the band width of the matrix at input stage and latter store the elements within the band width of cholesky lower triangle matrix at output sta.

作者针对地球物理数值模拟中常碰到的大型稀疏变带宽方程组的求解问题，介绍了一种大型稀疏变带宽矩阵的存储方法及 Cholesky分解法。

Using a method for storing the large-scale sparse matrix with varying band width, Cholesky decomposition, Green function and normalized least square fitting inversion, the paper improved the computing accuracy and efficiency in imaging calculation.

利用有限元方法实现了井间电磁成像，为了求取散射电磁场的积分方程组，运用了处理大型对称变带宽方程组的 Cholesky 分解法，反演时使用了格林函数和最小二乘法，既提高了反演速度又提高了反演质量。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

Finally, For the first time, the Ritz variational based mode matching method using new basis functions is proposed to deal with a discontinuity region. The general process to construct the linear equation group is developed, and the equation group's rank is only half of that of the cascading treatment. Thus the efficiency can be increased.

还首次采用新型基函数并利用里兹变分法和模式匹配法提出了构造处理一段不连续性问题的线性方程组的一般理论，方程阶数可比常规的级联处理方法降低一倍，可提高计算效率。

We will have focal point study for moving and fixing grid law etc., have the application to the free surface search of he impressure influent fields.

应用有限元对土石坝的二维稳定渗流进行了分析，选取变分原理和插值函数进行，建立了有限元方程组。

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

Based on the Maxwell\'s equations, the boundary value problem, variation problem, interpolation function and stiffness matrix in two-dimensional magnetotelluric are derived.

从麦克斯韦方程组出发，推导出二维大地电磁测深的边值问题、变分问题、有限单元法的插值函数以及单元刚度矩阵。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

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。

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。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。