查询词典 variational equation

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

Supposed stochastic variations are perturbed in a small range, we can get a nonlinear equation of these stochastic variations by using a Taylor series or a Neumann series expansion of the system matrix. The application of perturbation techniques translates this nonlinear equation into a pair of constant linear recursive equations. Then we have written a paper "Stochastic Finite Element Method for Interconnect Including Variational Analysis" which has been contributed to 11th Asia and South Pacific Design Automation Conference.

本文所取得的主要成果就是提出了一种新的算法，即用随机有限元来分析变化的互连线，将方程按随机变量泰勒展开或者纽曼展开，从而化无限维为有限维；应用matlab进行了算法仿真，并将结果与传统Monte-Carlo与GETA进行了比较；最后写了一篇文章《Stochastic Finite Element Method for Interconnect Including Variational Analysis》，已投第11届亚洲和南太平洋设计自动化会议。

In this paper, we present a class of equation model for image denoising and edge enhancement. The model is based on robust statistics error norm and variational theory. By analysing the parameters of the equation and designing the methods of module partitions, the numerical experiments reach a good result and the parallel efficiency has been improved remarkably with finite difference method.

本文基于稳健统计误差模函数及变分原理构造了一类用于图像去噪、增强边缘的方程模型，对相关参数进行了分析，设计了该方程有限差分数值求解的并行算法，并对分块模型及实现过程进行改进，提高了并行效率，在此基础上完成了并行数值实验，并对结果就误差模选取、并行效率等方面进行了分析。

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。

It is equivalent to solve differential equation for under water explosion. The modes of velocity potential function and movable boundary are chosen, then, a variational equation system is derived by REDUCE procedure on computer.

在此基础上，选取了流场及运动边界的模态，将泛函对选定的自变函数变分，并取驻值；用REDUCE语言由计算机推出变分方程组。

Based on the two phase anisotropic model this paper analyses and presents the dynamic equations of elastic wave propagation, the Galerkin variational equation, and the finite element equation in two phase anisotropic media.

基于双相各向异性介质模型，首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程，然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件。

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 paper aimed at resolving the question of side value of Laplace equation and Poisson equation in plane angular domain by using integral equation of the solution of mathematic physics equation.

旨在利用数学物理方程解的积分公式，去解决平面角形区域内Laplace方程和Poisson方程的边值问题，而其关键在于构造相应域内的格林函数。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

This model consists mainly of four kinds of simple line equations such as water level equation,velocity equation,auxiliary equation and initial equation.

该模型主要由水位方程、速率方程、辅助方程和初值方程这4种方程组成，它们都是一些简单的线性方程。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。