求解

The problem of solving linear equations changed equivalently into the problem of searching the minimum of unconstrained optimizations of function by variation principle in the paper.

首先通过变分原理将求解线性方程组的问题转化为等价的求解无约束函数最优化问题的极小值。

In the chapter 2, based on elastic mechanics and variation principle, the fundamental and process of static and dynamic FEM is presented, placing special emphasis on the modal superposition method.

第二章根据弹性力学和变分原理，系统总结了有限元法求解静力学、动力学问题(包括特征值、动力响应问题等)的基本原理和步骤，并重点对模态叠加法求解动力，响应问题作了阐述。

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

This method can ensure to obtain all reasonable solutions meeting the fault equation, can be applied for various fault correlation criteria (such as various residual vector norm criteria) and underdetermined fault equation, and the algorithm is very simple and facile, not necessary to compile specific program for every particular condition.

首先给出求解故障方程的Monte Carlo算法，该算法能够保证得到满足故障方程的全部合理解；能够简单地用于各种故障相关性准则(例如各种残差向量范数准则)以及亚定故障方程的求解问题；并且算法简单易行，无需为每个特定情况专门编制计算程序。

Another is that retaining the refined Ritz vector in the new subspace,calledaugmented Krylov subspace.This way retains useful information and makes theresulting algorithm converge faster.

改进后的求解子空间为一增广Krylov子空间，该空间中包含更丰富的特征向量信息，因此用精化Arnoldi方法在该空间上求解矩阵特征问题时收敛速度更快。

In the sense of Von Karman large displacement, the governing equation of nonlinear dynamic response of the clamped circular plates under impact of a mass is established by using the virtual displacement principle and Galerkin's method in this paper. The effect of coupling between the impact load and the displacement of. the circular plates is considered. The governing equation is solved by applying the time increment method and the singular perturbation theory, and the asymptotic solutions of nonlinear dyna...

本文在Von Kármán大位移的意义上，利用虚位移原理伽辽金方法建立了圆板在物体撞击下的非线性动力响应的控制微分方程，在研究响应问题时，考虑了冲击载荷与圆板位移响应之间的耦合影响，文中使用时间增量法和奇异摄动理论求解问题的控制方程，获得了固支圆板非线性动力响应的近似解，并且求解了具体算例，绘出了圆板位移、应力响应曲线以及冲击力随时间的变化曲线。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

In the inversion process, an improved GaussSadel interative method with a weight coefficient determined according prism's berried depth is introduced.

本文采用改进的高斯-赛德尔迭代求解磁化强度矢量层析成像方程，在求解方程中引进了与深度有关的权系数。

The alterative direct iterative, strong implicit procedure, preconditioning transpose-free variant of quasi-minimum residual method and biconjugate gradient stabilized method of the Krylov subspace methods were implemented in SIMPLER algorithm to solve the algebraic equations.

将交替方向隐式、强隐及Krylov子空间法中的TFQMR、Bi-CGSTAB方法实施于SIMPLER算法，作为其内迭代求解方法，比较了不同代数方程求解方法的收敛速度，并首次分析了它们对算法健壮性的影响。

Based on the Flory-Huggins theory, the binodal, spinodal and critical point equations for polymer-solvent-nonsolvent system are derived in detail.

以Flory-Huggins理论为基础，详细推导了聚合物－溶剂－非溶剂三元聚合物成膜体系的双节线、旋节线和临界点求解方程，提供了方程的求解方法。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。