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The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算,将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程,再由反射图方程和图像梯度信息构造目标方程,进而用Newton迭代算法求出该方程的数值解,得到表面三维形状。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型:1 根据造波板做椭圆余弦运动或正弦运动速度,推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件,数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确;2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解,讨论了该解析解的适用范围;3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用;4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

Methods In the first place,the mathematical model of the dynamical response of viscoelastic thin plates is established in physical space,then the fundamental equation in Laplace domain is obtained by using Laplace transformation.

首先在物理空间建立了粘弹性薄板动力响应问题的数学模型,然后利用拉普拉斯变换得到拉氏变换域的基本方程;利用基本方程的基本解,由边界元方法得到边界积分方程,并求得数值解;最后通过数值 Laplace 逆变换得到原问题的解。

For the plane wave of laser without pulse shape, we derive the express of electron trajectory by the relative Lorentz and energy equations. Note that the orbit of electron becomes a "fat-8" in the average rest frame. For the plane wave of Gaussian laser, we may know that, through relative Hamilton-Jacobi equation, electrons are accelerated in the front of pulse and decelerated backward. Whereas for the non-plane wave of Gaussian laser, we solve the Lorentz and energy equations by fourth order Runge-Kutta method.

对于无脉冲形状的激光平面波是从考虑了相对论效应的Lorentz方程和能量方程出发,得到了电子的运动轨迹方程表达式,在纵向平均速度参照系下该电子的轨迹呈现"8"字形;对于高斯型单色激光平面波是从相对论Hamilton-Jacobi方程出发,得到激光平面波在脉冲前沿加速电子而脉冲后沿减速电子,电子能量增益为零;而对于高斯型单色激光非平面波是从拉格朗日运动方程和能量方程出发,通过四阶Runge-Kutta法数值求解,得到电子在纵向有质动力、横向电场作用下加速电子,最后在强大的横向有质动力作用下从脉冲侧面散射出去,可以获得很大能量增益本文得到了相应的电子瞬时动量解析表达式。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论,并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法,其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法,最后,介绍了两类数值求解非线性微分方程问题的方法。

Therefore,it is necessary to research diffusion equation for suspended sediment because it describes the sediment move process in the water body.The equation is a various coefficients second-order linear partial differential equa-tion,such equation under complex boundary condition is very difficult to get its analytical solution,while its numerical solution relative analytical solution is more easier and has the obvious superiority:simple,the computation convenience.but to get a kind of difference format which is good accuracy and stability is not easy.

泥沙扩散方程实际上是一个变系数的二阶线性偏微分方程,这样的方程在各种复杂边界条件下求解是十分困难的,求它的解析解在数学上存在着难以克服的障碍,无法求出其精确解,因此常用数值方法求它的近似解,相比较而言,数值方法有着明显的优势:即简单灵活、计算方便快捷,但要寻找一种精度高、稳定性好、计算方便的差分格式也并非易事。

The main contents include the ray phenomenon and its generation conditions; the deduction and physical illumination of wave action conservation equation and wave number conservation equation; ray theory for sinusoidal waves; Fermat's principle; the variation of amplitude in the case of straight and parallel depth contours and circular depth contours; the amplitude near the caustics; wave trapping; deduction of mild-slope equation and the relevant numerical solution methods.

讲授折射现象及其发生的条件;波作用守恒方程和波数守恒方程的推导及物理解释;稳恒正弦波的控制方程及射线方程;费马原理;利用射线方程研究等深线是平行直线和圆周线时波振幅的变化,特别是焦散线附近波高的变化以及由此而产生的波的俘获;缓坡方程的推导及有关的数值求解方法。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究: 1)建立了推广形式的共轭变分同化方法,使之能够应用于LAGFD-WAM海浪数值模式; 2)导出了扰动谱线性演化方程,分析了扰动谱增长、衰减机制,考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程; 3)利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布; 4)将推广的共轭变分方法应用于海浪谱能量平衡方程,建立了连续形式的海浪同化模型,特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式; 5)分别进行了波谱层次上和有效波高层次上的同化试验,并对数值结果进行了分析。

In this paper, the generator model of constant transient voltage and the invariableness impedance model was used, and the saliency of generator is included; through the analysis of the characteristic of the network equation calculation in the transient stability analysis, a new node ordering algorithm is proposed. Better initial value can accelerate the convergence rate of the networking equations, reduce the number of iterations, thus to cut down the amount of calculating time.

本文首先建立了适合于暂态稳定分析的简单模型,其中发电机采用E_q恒定模型,考虑了发电机的暂态凸极效应,负荷采用恒定阻抗模型;研究了电力系统的暂态稳定分析方法,指出目前数值积分暂态稳定计算方法中存在的不足,主要是网络方程的求解速度过慢;分析了暂态稳定计算中网络方程的特点,将稀疏技术应用于网络方程的求解,提出了一种新的节点编号方法——最小度最小有源节点道路集算法,减少了网络方程的计算量;在进行交替迭代求解时,将预测算法应用于每一积分步网络方程功角和电压的初值估计当中,应用自回归算法和广义延拓算法,期望给出一个更有效的电压和功角初值方案,来加快方程的收敛过程,减少方程迭代的次数,以提高计算速度。

First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soil were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth,and the state equation was established by Hankel integral transform method,furthermore the transfer matrixes within layered media were deriv...

首先,通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组,基于径向Hankel变换,建立问题的状态方程,求解状态方程后得到传递矩阵;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例。

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Plunder melds and run with this jewel!

掠夺melds和运行与此宝石!

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻,也许正是在通往天国的路上,我体验着这白色的晕旋。

When you click Save, you save the file to the host′s hard disk or server, not to your own machine.

单击"保存"会将文件保存到主持人的硬盘或服务器上,而不是您自己的计算机上。