数值方程

In this paper, combining the technique of parallel computation with the numerical method of 3D eddy current field, we designed the algorithms of generating mesh, forming finite element equations and solving them in parallel on a shared memory multiprocessor (SGI Challenge L 8 CPUs), and presented a concrete and effective method.

本文将并行计算技术和三维涡流场计算方法相结合，对三维涡流场有限元分析的并行处理技术进行了细致的研究，设计了基于共享内存并行计算机(SGI Challenge L 8 CPUs)的网格剖分并行算法和三维涡流场有限元方程形成和求解的并行算法，为数值求解实际三维涡流问题提供了一种有效途径和具体方法。

The spectral element method, which combines the high-order precision of spectral methods and the geometrical flexibility of finite element methods, has achieved great success and is becoming a useful tool for investigation of such equations.

谱元法作为一种高阶的数值方法，结合了谱方法的高精度和有限元法灵活的网格剖分技术，在不可压流体的计算中已取得了很大的成功，并正成为计算随机微分方程的一个有力工具。

The influence of the parameters such as the grid shape and size, parameters of equation of state and artificial viscosity coefficients, etc.

通过数值模拟分析了网格形状、网格密度、状态方程参数、人工粘性对计算结果的影响。

On the other hand, the Hall effect in the process of magnetic reconnection isstudied respectively through numerical simulating and theoretically analyzing.

另一方面，本文运用Hall MHD方程还对磁重联过程中Hall效应进行了数值模拟研究和理论分析。

A two dimensional stochastic nonlinear dynamical model of semi-active suspension system is presented considering the stochastic factor of the road. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the stationary stability is studied by solving the Fokker-Planck-Kolmogorov equation. The Backward Kolmogorov equation for reliability function had been established.

考虑路面随机因素的影响，首先建立二自由度汽车半主动悬架的随机非线性动力学模型，运用随机平均法，将Hamilton函数表示为一维扩散过程，并运用奇异边界理论分析系统的全局随机稳定性，建立可靠性函数所满足的Backward Kolmogorov方程，结合初始条件和边界条件得出数值结果。

The thesis analyzes the quantum properties of the soliton combining the analytic and numerical method. It includes the following several parts (the bold parts are creative work): 1. We obtained the quantum field equation of optical soliton in the lossy fiber by means of heat reservoir theory.

本论文采用解析与数值模拟相结合的方法来分析孤子的量子特性，主要内容包括以下几个方面（黑体部分属于创新性的工作）： 1、用热库理论得到了考虑光纤损耗的光孤子传输的量子场方程。

The existence and uniqueness of the solution to the equation are verified based on the homeomorphism theory, and an example is given to show the rationality of the solution.

数值求解拟线性抛物型偏微分方程边值问题通常可归结为解非线性方程组，非线性方程组解的存在与惟一性是解方程组的前提。

Numerical simulation of cavitation in axial-flow pump under large-flow condition has been conducted by calculation Eulerian-Eulerian homogeneous model and Navier-Stokes equation with RNG turbulence model in this paper.

江苏大学能源与动力工程学院，江苏镇江 212013摘要：本文利用Navier-Stokes方程、RNG 湍流模型和欧拉-欧拉均相流模型，对轴流泵偏大流量工况下的空化流动进行了数值模拟。

However, they did not give the numerical method for computing the homogenization parameters and solve the homogenization equation.

然而，他们没有给出计算均匀化参数和解均匀化方程的数值方法。

By using the theories of conservation of momentum,conservation of energy and hydrokinetics,a mathematical model for describing the relationship among the fluid parameters,the formation parameters and the vibrant operation parameters was established.The analytic solutions of one-dimensional and radial transfusion equation for compressive and single-phase fluid flow through the compressive formation were obtained.The effects of each parameter on the vibrant operation were also gotten.On the basis of the above results,the computation models were established.

应用动量守恒、能量守恒、流体动力学等基本原理，建立了地层参数、流体参数和振动作业参数之间相互耦合的数学模型，求出了单相微可压缩流体在可压缩地层中的平面一维和平面径向渗流方程的解析解，得到了各项参数与振动作业效果之间的关系，为振动采油的数值模拟提供了初始压力分布表达式。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新