数值方程

B Using the basic solutions of single inclusion and single crack, singular integral equations of plane interaction problem of line inclusion and line crack have been deduced. Numerical method is set up. Expresesions of stress intensity factor of both inclusion and crack and interface stress of the inclusion are given.

使用单夹杂和单裂纹的基本解，导出了线夹杂与线裂纹相互作用平面问题的奇异积分方程，并为其建立了数值法，给出了夹杂与裂纹端点的应力强度因子及夹杂两侧界面应力的表达式。

In this dissertation, the numerical method solving the model equation influid motion in some sense has solved some tough problems which traditionalmethods cannot, as in the case of capturing shockwave, enhancing resolution, andspeeding computation. In terms of capturing shockwave and enhancing resolution,this method has proved to be superior to difference method; in terms of speedingcomputation, superior to TVD scheme. Particularly, it is highly effective to solveodd singular solution problems.

本文研究的求解描述流体运动的若干模型方程的数值方法，在一定程度上解决了传统方法在某些方面的难点问题，如在捕捉激波、提高分辨率方面优于差分法，在计算速度方面优于TVD格式，特别是对处理有奇异解的问题很有效。

With the use of the dislocation method of complex potential function, this paper studies the interaction between the interface macrocrack and the interface or beneath-interface microcracks by the construction and numerical solution of singular integral equations .

采用复势函数的位错解方法，通过对奇异积分方程的建立和数值求解，研究了界面主裂纹同界面及基体微裂纹之间的干涉。结果表明远场载荷角ψ同Dunder's参数α对界面微裂纹及基体中水平微裂纹同主裂纹干涉的影响都很显著，而ψ对屏蔽区的影响则远小于α对其的影

According to these, transient simulations of several water and hydraulic engineerings with Press-Regulation facility has been studied. Such as Air-Cushioned Surge Chamber , Inclined Ceiling Tailrace, Siphonic Pump Station. And then some reference conclusions are offered.

因此论文主要通过数值模拟对带有变顶高尾水隧洞、气垫式调压室、虹吸断流等调压设施的水利水电工程过渡过程进行了深入的研究，并对带有调压室的复杂管系水轮机调节系统建立了状态方程，得出了对工程设计及动态仿真研究很有参考价值的结论。

The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation.

模式的主要数值方法包括：分别以拟频谱法以及二阶有限差分法近似控制方程与边界条件中的水平与垂直导数；以二阶Runge-Kutta法进行非稳态的自由液面位移与流场速度的时间积分；利用改良式割线叠代法求解计算区间中不可分离的压力Poisson方程式，以满足不可压缩流条件。

With the development of science and project technology, more and more questions need the solution of big linear systems. This solution is one of the fastest ways for researching numerical algebra, especially for the big sparse matrix.

随着科学和工程技术的发展，越来越多的问题需要求解大规模的线性方程组，对这类方程的快速求解已成为数值代数研究的热点之一，特别是具有稀疏结构的大型方程组的求解。

A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods.

对于球几何问题，讨论了一种基于微分方程的变分形式求解方法，数值计算显示达到了较满意的精度，而且计算过程比起其他近似方法要简单

The false scattering and ray effect in spherical harmonics method ,including P-1 and P-3 approximation,is studied.

从辐射传输方程的近似求解过程出发，在定性分析的基础上构造物理模型，通过数值模拟研究球谐函数法(P1和P3近似法)的假散射和射线效应。

Some applications of spline functions in numerical solutions of differential equations are discussed in this dissertation.

本文讨论样条函数在微分方程数值解中的一些应用。

By the numerical simulations of the free surface velocity histories and based on the best consistence between the computational results and the experimental ones, the material parameters in the damage evolution equation and the spoliation criterion are obtained.

通过自由面速度历史的数值模拟，并基于计算结果与试验结果间的最佳一致性，得到了损伤演化方程和层裂准则中的材料参数。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。