变分法

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

To variational inequalities with separate structures, the thesis presents a descend method based on the alternating directions method, and some numerical results demonstrate that the new method is effective in practice.

对于结构可分的变分不等式，本文在交替方向法的基础上提出了一种下降方法，并给出了相应的算法收敛性证明与数值试验结果。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

HJB equation; quasivariational inequality; domain decomposition; convergence; iterative algorithm; relaxation algorithm; existence; multigrid method

基础科学，数学，数学分析HJB方程；拟变分不等式；区域分解；收敛性；迭代法；松弛算法；存在性；多重网格法

The influence of consolidation is analysis by the improved transfer function method and finite different method that is used to calculate the consolidation degree.

本文运用差分法计算变荷载下多层地基的固结度，进而结合上述改进的传递函数法分析固结对路堤桩的影响。

By the principle of penalt function, the irrotational fluid field is constrained, and author has proposed the Difference Method for distinguishing fluid vortex modes among the natural modes of coupled systems. Author has calculated the real frequencies with the extra deductive method, and discussed the influence of the numerical solution due to the irrotational constraint.

对于流体有限扰动时的非线性耦合系统的有限元分析作了一些探讨，给出了非线性系统的基本方程、变分原理及有限元方程，并具体地导出了三维几何非线性流体单元的切线刚度公式，采用增量形式的Newmark预报——校正逐步积分法计算系统的动力响应，由Newton-Raphson迭代法及其修正方法求解系统的非线性方程组，还列出了不平衡力余量检查和位移迭代增量检查等迭代收敛判断准则。

Magnetic field method is used to analysis the distribution of multi-medium, complex boundary, large difference in dimension, non-linear and forced axial symmetry magnetic field in magnetic fluid seal, the data is derived by unequally spaced net finite difference, and the results of different structure are showed by magnetogram.

利用变步长有限差分法对磁场法描述的磁流体密封中磁介质多、边界复杂、尺寸差别大、非线性的强磁场进行求解，得到了多种形式密封结构磁力线和磁感应强度等值线的分析结果。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

Then, a comparison is made between Undermined Lagrange Multiplier Method and Substitution Method, and it explains that these two methods have the same actions on cancelling and releasing restrictions.

比较了变分学中的Lagrange乘子法与代入法，说明二者在消除约束和放松约束方面具有相同的作用。

By means of analysis of the influence of barrel inner surface on firing process and firing precision,3 kinds of exact manufacture method were proposed,they are compulsive spiral flow method,high pressure water jet ringed flow method and magnetorhelogical fluid method.

通过分析身管内表面对射击过程的影响后，提出了3种精密加工的方法，分别是强制螺旋流法、高压水射环流法、磁流变液法。

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。