查询词典 variational equation

We give the fundamental solution of adjoint transport equation and take it into variational form.

给出伴随输运方程的基本解，再将其带入变分形式中，对关于空间和角度的两个积分进行化简。

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

Still based on Ciarlet-Raviart mixed variational principle, this section gives the mixed finite volume element scheme for biharmonic equation on rectangular partition.

综合有限元方法及有限差分方法的优点，李荣华教授于二十世纪八十年代初提出了广义差分方法，亦称为有限体积元方法。

It is related to the variational inequality problem, bilinear programming, nonlinear equation. So there is actual meaning and theories value to study how to solve it.In recent years, many algorithms for solving the generalized linear complementarity problem are put forward. But they basically belong to the traditional iterative methods, and may not be efficient since the computing time required for a solution is greatly dependent on the dimension, structure of the problem and the complexity of the algorithm used. Different from the traditional algorithms, the neural network has many advantages on calculations and real-time applications for its inherent massive parallelism and electric circuit implementation.

近年来，人们对广义线性互补问题提出了许多算法，但这些方法基本上属于传统的迭代法，由于它们的计算时间极大地依赖于问题的规模、维数以及所使用的算法，因此很难满足实时并行的要求，与传统数值方法不同，由于内在的并行分布处理信息的特点及电路实现的潜能，神经网络有着许多计算上的优势和实时性的应用，自Hopfield提出著名的人工神经网络模型-Hopfield神经网络，并将其成功应用于优化问题后，用神经网络求解优化问题得到了相当深入的研究，并取得了许多重要的成果。

However,authors still do not find the relevant references on convergence and symmetric problems of the semi-analytical solution.Based on the semi-analytical solution for Hamilton canonical equation theory,the formulations of the clamp and simply supported and symmetric boundary conditions on the Hamiltonian element are derived by the variational principle.Several numerical examples show that with increase of meshes,the convergence rate of the semi-analytical solution is faster than the convergent rate of traditional finite element method based on displacement.

①在厚度上没有任何位移和应力模式的假设，由于传递矩阵方法的引入，从理论上讲，不受板壳厚度或层合板壳层数的限制；②采用弹性力学的Hamilton正则方程半解析法，可以克服边界的局部化效应[8]；③由于在平面内或圆柱壳的曲面内采用了有限元法，所以一般的板壳问题不受结构侧面边界条件的限制，在复杂工程板壳问题上具有广泛的应用领域。

Firstly, the modified H-R variational principle for elastic material was briefly presented, then the quadratic interpolation functions were used to express the out-plane stresses and displacements variables, consequently the formulation of 8-node isoparametric element for Hamilton canonical equation was derived in detail.

首先简要地介绍了弹性材料修正后的H-R变分原理，然后用二次插值函数表示平面外应力和位移变量，并详细地推导了Hamilton正则方程的八节点等参元列式。

These problems include the selfadjointness of the coefficient matrix operator, the functional of the matrix operator equation, the equivalence between variational problem and boundary value problem of eddy-current fields, and the extreme value principle of the functional.

本文首先从求解时谐涡流场的〓-ψ法与〓-Ω法的矩阵算子方程出发，提出了时谐涡流场的统一矩阵算子方程，进而系统地讨论了该方程的系数矩阵算子的自伴性、矩阵算子方程的泛函、涡流场边值问题与对应变分问题的等价性以及泛函的极值原理。

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 method uses expansion in terms of scaling functions to approximate the axial field component and transforms the field equation into a matrix equation by applying a variational formulation.

在该方法中，用尺度函数把场分量近似为级数，通过变分公式把波导问题化为矩阵方程。

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。