数值微分

Since the initial start of buried pipelines results in three-dimen-sional unstable heat transmission , and at initial start the temperature change of the soil around a pipeline is affected by the temperature inside the pipeline and the ground surface temperature annual fluctuation, the differential equation for heat transmission and the boundary value may be line...

埋地输油管道启输过程是三维非稳定传热问题，启输过程中管周土壤温度场的变化受管内热水温度和启输前地表面温度年波幅的影响，可将传热微分方程和边值条件线性组合成两个定解问题，用电子计算机进行数值求解，得出计算公式，以确定预热阶段管路任一点任一时刻的热水介质温度。

This thesis presents the studies of U-shape gantry structure of container gantry crane, and dynamic simulation and fatigue life estimation of its rigid anti-sway. The main contends are as follows: Supposed that trolley frame is composed of spring structure, due to larger trolley gauge of U-shape gantry structure. For the gantry crane, a series spring dynamic vibrating model with three masses, three freedoms of degrees is built in this thesis and vibrating calculus equations are precisely resolved by mode analyses rule.

本文研究集装箱门式起重机U型门架结构及其刚性减摇系统的动态仿真和疲劳寿命估算，主要内容如下：由于U型门架结构小车轨距较大，本文建立了考虑小车架为弹性结构时门式起重机的三质量三自由度串联弹性动力学振动模型，用模态分析法求解振动系统微分方程组的数值精确解。

Variation laws of the film thickness with rotor angle, angle of swash plate, pocket pressure and pressing force were obtained. The differential equations of the variation of the film thickness were established, hence the dynamic law of the film thickness in one period was further obtained.

通过数值计算，得到了排油区滑靴油膜厚度与转子转角、斜盘倾角、油池压力、柱塞压紧力之间的变化规律，建立油膜厚度变化的微分方程，给出在吸、排油一个周期内，滑靴油膜厚度的动态变化规律。

Finally the numerical results are presented to confirm the effectiveness of Gauss-Seidel parallelized with alternate tiling method,specifically compared with owner-computing and red-black Gauss-Seidel methods,and show that the new parallel iterative method has better parallel efficiency as well as scalability.

许多物理应用问题的求解都归结为求微分方程数值解，其核心是高效地求解线性方程组，GS(Gauss一Seidel)和SOR迭代算法以其高效性和实现简单的特性成为大型线性方程组求解的重要算法，并且常用作非定常迭代算法的高效预条件子，是许多应用软件的核心算法之一。在并行处理系统

This paper elucidates the necessity of introducing differential geometry in the quantitative study of structural geology and discusses its applications in the quantitative study of structural geology and relevant numerical calculation method.

中文摘要：阐述了在构造地质学定量研究中引入微分几何学的必要性，并讨论了在地质构造定量研究中的具体应用及相关的数值计算方法。

This paper presents the explicit expression of geodesic equation on a paraboloids of revolution using differential geometry which avoids the complexity of geodesic ray tracing by numerical approach.

本文根据微分几何原理，从广义费马原理出发，得到了旋转抛物面上短程线的解析式，避免了数值方法射线寻迹的复杂性。

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。

The author systematically studies the construction principle of high order accuracy difference scheme and uses third-order accuracy Godunov scheme with TVD property to solve three-dimensional viscous flow field in cascade.

为了减少网格畸变对数值解的影响，发展了一种微分方程法与代数法相结合的网格生成方法。

In the optimization iteration, the levelset function values of nodes are considered as design variables. To computedifferences normally, the Heaviside function is handled for smoothing, theregularized Heaviside function is selected to avoid the oscillation inhomogenizations method, and the results can converge smoothly.

在优化迭代过程中，节点上的Level Set函数值被看作是设计变量，并且为了便于微分计算能够正常进行，对Heaviside函数及其导函数做了光滑化处理，选取了一种正则化的Heaviside函数，避免了均匀化方法中出现的振荡现象，可以平稳地收敛到最终结果。

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。