数值计算

As important ways for numerical solutions of partial differential equations, spectral methods have been developed rapidly in the past several decades. They not only have been widely applied to numerical simulations in various fields such as physics, mechanics, aerology, oceanics etc, and their theories of numerical analysis also tend to perfect.

作为数值求解的一种手段，谱方法在近几十年得到了蓬勃的发展，它不仅被广泛运用于物理、力学、大气、海洋等领域的数值计算，而且它的数值分析理论也不断地趋于完善。

It shows that a remarkable advantage of the symplectic methods applied to the Schrodinger equation is the precise preservation of charge conservation law. In order to study the numerical stability, we also adopt the different time step sizes.

为了比较，我们还给出了同阶的非辛算法的数值模拟，从而得到辛摄动配置算法和其在理论上等价的辛龙格-库塔方法在数值上的等效性以及辛算法在数值计算中的优越性。

Thus, non-negative property is suggested as the criterion of stability. Further, diffusion coefficient is replaced by an artificial one in the finite difference equation to simulate the entropy generation can improve the accuracy of the numerical analysis.

在尽可能满足对流扩散过程数值格式中的输运性或守恒性及稳定性的同时，以扩散熵产仿真为原则的伪扩散系数可有效地提高数值模拟的仿真性，为数值计算中扩散系数的修正提供了一种有效的手段。

With the development of computer technology and numerical modeling techniques, many numerical methods have been established and applied to this field. Finite element method is one of the most effective.

随着计算机科学和数值计算方法的发展，目前已经有很多数值方法应用于大体积混凝土结构温度应力仿真分析中，其中有限单元法是一种十分有效的数值分析方法。

Finite difference method is adopted in this model to analyze the temperature distribution and fulgurite resistance of a fuse.

针对所提出的简化模型，用直接差分法进行数值模拟，设计出用直接差分法进行数值计算的通用程序，实现了温度分布和弧后残躯电阻的数值分析。

The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also first or higher orders derivatives.

数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度。

The effect of the elastic-plastic matrix of friction soil with nonrelevant flow rule on the numerical convergence of finite element method is analyzed in this paper; and the effect of elastic modular, poisson ratio and earth pressure coefficient on numerical results are studied in this paper. At the same time, the hybrid element with a mixture of displacement and stress variables and the conventional element with solely displacement variable are compared when used in geomaterials.

在ABAQUS有限元分析软件的基础上，本文研究了服从非关联流动法则摩擦性土体的弹塑性矩阵对有限元数值算法的影响，并研究了弹性模量、泊松比以及地基土压、力系数对数值计算结果的影响，同时探讨了数值分析过程中常规位移元与杂交元在岩土工程中的应用。

As an effective method of numerical computation, FEM is widely applied in numerical simulation of metal deformation process.

有限元法作为一种有效的数值计算方法已经被广泛应用于金属成形过程的数值模拟方面，但是有限元分析软件在使用过程中也存在许多问题，例如数值模拟解的精度问题，直接优化设计技术参数的问题。

In this project, we develop the numerical model of the differential quadrature element analysis of beam problems considering the effects of shear deformations. The results demonstrate this method.

在这个计画中我们开发剪变形梁问题的数值积分表示微分元素分析的数值模式，并做数值计算，证明此种方法的优越性。

In this paper, we consider the following computing method of tridiagonal matrix:(1) decoupling of linear equation;(2) determination of determinant and eigenvalue-eigenvector relation;(3) matrix inversion.

二引宫在数值计算中，有许多问题足后归结为三对角矩阵的计算涸此研究它们的计算方法是有意义的。此外，有些三对角阵的计算方法可以做为带状阵计算的借鉴。

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。