有限差分运算

But it demands the higher computational accuracy. Time-dependent LU-SGS method and close coupled full implicit finite volume scheme are used. The AUSMPW+ based on the three-order MUSCL difference scheme is used for the inviscid operator, and the maximum eigenvalue splitting method is used to convert matrix operation to algebraic operation in order to shorten the computing time.

运用时间相关的LU-SGS方法，采用强耦合的全隐式有限体积进行离散，其中无粘对流项采用三阶MUSCL型差分的AUSMPW+格式，并应用最大特征值分裂，将矩阵运算转化为代数运算，大大缩短了计算时间。

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。

Took Chongqing Gong-he tunnel as an engineering example and studied the failure mechanism of surrounding rock and the correlation with bolt support system by using the methods of theoretical analysis, modeling test, numerical simulation and in situ test, some helpful conclusions were arrived as follows.Firstly, a new failure criterion for transversely isotropic rock mass was proposed with consideration of bedding plane orientation and major principal stress, and the corresponding algorithm, arrived through VC++6.0, can be easily embedded into the software FLAC3D for the geotechnical calculation.

论文在国家自然科学基金专项基金创新群体基金项目(No.50621403)以及国家自然科学基金重点项目"隧道与地下空间工程结构物的稳定性与可靠性(No.50334060)"的资助下，以共和隧道为示范工程，运用理论分析、物理模型实验、数值模拟和现场测试等手段，对共和隧道大埋深段层状岩体的围岩变形破坏机理、锚杆支护力学效应及围岩-支护结构的变形特征等内容进行了研究，其主要研究成果有：①在总结和探讨国内外学者提出的层状岩体经验型连续介质破坏准则基础上，结合层状岩体力学特性，考虑层面方向和最大主应力方向两个影响因素，提出了共和隧道层状岩体横观各向同性破坏准则；采用汇编语言VC++6.0实现了横观各向同性弹塑性本构关系的算法，并嵌入FLAC3D有限差分数值分析软件接口中实现数值运算。

The first is on the study of spectra technique in boolean function and in its probability function.

得到布尔差分等布尔运算在此映射下的实函数运算，并用有限离散变换实现了从原函数到象函数、到象函数偏差分，以及到布尔差分的象函数的变换，并研究了这一系列变换的性质。

When discrete characteristic of digital images is considered, finite difference approximates differential operator.

考虑数字图像离散化特征，用有限差分近似微分运算，将由PDE描述的反射图方程转化为关于未知高度的代数方程，然后使用迭代算法求解，得到新的SFS算法。

To observe global/local failure in macro- and micro-scope respectively, and to speed up numerical approach for some cases, this research also tries to combine PFC2D software with the finite difference method of FLAC code to carry out three issues:(1) uniaxial test; and (2) Brazilian test to assess this linking/coupling numerical algorism, then (3) indentation fracture test in rock by a single-cutting tool.

本研究并於国内首次使用分离元素法软体PFC2D与有限差分法软体FLAC两二维数值软体进行贯切破坏之数值耦合运算，利用耦合概念加速分析之运算速度，两软体之连结透过力与速度之交换传递。

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。