数值

As a fast TDIE solver with high accuracy and efficiency, plane wave time domain algorithm is studied deeply in this thesis. The implementations of two-level and multilevel PWTD-enhanced MOT schemes are described and the numerical efficiency is presented.

论文还深入研究了一种高精度、高效率的TDIE加速算法——时域平面波算法的理论基础、数值实现的关键技术，以及两层、多层PWTD加速MOT的实现方案、程序流程以及数值性能。

In Chapter 7, we present some numerical results of our method for image reconstruction problems. Results of two singular problems related to the Poisson equation are also given.

第七章，主要是给出我们的算法在图象重构中的具体应用的数值结果，同时还给出了两个有关Poisson方程的奇异问题的数值结果。

In the computational methods of TPBVP, in order to reduce some difficulties involved in solving a TPBVP via adjoint variables, we discuss a direct method in which state and control variables are indirectly parameterized, The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and control variables, thus converting the optimal control problem into a nonlinear programming problem, which can be solved numerically.

在数值解法中，为了减少解决两点边值问题共轭变量带来的困难，主要讨论了将状态变量和控制变量进行参数化的一种直接方法，这种方法采用了近段发展起来的使用分段的多项式来代替状态和控制变量的直接优化方法，然后最优控制问题就转化成可以用数值方法解决的非线性规划问题，使得迭代初值更加容易选取。

Contact-impact model and its discrete schemes for revolute pairs with small clearances ;2. Based on the theory of contact dynamics,the dynamic model with clearances of sizing press roll was established using the method of numerical simulation.

基于接触动力学的理论，利用数值模拟的手段建立了调宽机含间隙的动力学数学模型，采用定步长四阶Runge-Kutta数值积分的方法，详细研究了运动副内间隙对接触力的影响规律。

Based on the theory of contact dynamics, the dynamic model with clearances of sizing press roll was established using the method of numerical simulation. The paper studied the effect of clearances on contact force inner Mechanism joints detailedly by the method of numerical integration of fix step length four orders Runge-Kutta.

基于接触动力学的理论，利用数值模拟的手段建立了调宽机含间隙的动力学数学模型，采用定步长四阶Runge-Kutta数值积分的方法，详细研究了运动副内间隙对接触力的影响规律。

The calculating results which predict that the tip undercooling decreases continuously with an increase of the primary spacing and no minimum undercooling exists have lent an obvious evidence to the above theoretical analyses. The tip undercooling changes sharply for the low primary spacings but slowly for the large spacings.

本文提出的数值模型表明，Peclet数较小时，可以将强制性枝晶生长处理成自适应边界条件进行数值计算；计算结果充分证实了上述的理论分析，并指出顶部过冷随一次间距的增大而连续减小，不存在最小过冷值；一次间距较小时顶部过冷变化显著，较大时变化缓慢。

Based on our own simulation results and results of some numerical simulation of single Fold structure by other investigators in recent years, the factors that affect single fold shapes and the variation of maximum principal stress and horizontal strain during the deformation of single fold are discussed in this paper.

本文结合近年来单层褶皱构造数值模拟研究进展，以及笔者近几年来对单层褶皱所进行的数值模拟实验研究，主要论述了单层褶皱变形的影响因素，单层褶皱变形过程中的最大主应力与水平应变的变化及其影响因素等。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

In probability sampling, a statement of the likelihood that a range of [size=+0]value s i.e.

在随机抽样中，它代表了一组数值成为真实人口数值的可能性。

In probability sampling, a statement of the likelihood that a range of values i.e.

Confidence level：置信度在随机抽样中，它代表了一组数值成为真实人口数值的可能性。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新