非数值算法

Because the derivation of the extended system has a block lower triangular form, the method of splitting iteration is applied to compute simple bifurcation point, not only computational work is reduced, but also local quadratic convergence is achieved.

由于所构造的扩充系统的导数具有分块下三角形式，采用分块迭代的方法进行数值求解，不仅减少了计算量，而且是二次收敛的，从而为Navier-Stokes方程非退化简单分歧点的数值逼近提供了有效的算法。

First, we discuss the noncharacteristic Cauchy problem for 1-D heat equation.

首先，对一维的热传导方程的非特征Cauchy问题，我们利用边界积分方法将问题的求解转化成解积分方程组的问题，再对积分方程组进行离散化来数值求解，最后的数值结果表明我们的算法是有效的。

This paper uses the non-uniform grid model successfully to fulfill the three-dimensional simulation modeling of the double post-hole convolute whose structures are complex; uses strut to fulfill the load modeling of the computer implementation; explores the feasibility and application value of using MPI parallel algorith into the simulation.

成功地使用了非均匀网格模型，实现了对结构复杂的中心汇流区的三维数值建模；运用金属支撑杆模型，实现了负载的数值建模。探讨了MPI并行算法运用到模拟中的可行性及其应用价值。

Based on the Navier-Stokes equations in conservative form derived with respect to nonorthogonal curvilinear coordinates and nonorthogonal velocity components, the numerical method for solving 3D viscous flow has been discussed.

本文基于非正交曲线坐标与相应的非正交速度分量下导得的守恒型N—S方程，讨论了求解三维粘性流动的数值方法，计算中显式时间推进算法与Baldwin—Lomax湍流模型被采用，应用本工作发展的程序，作为算例计算了一个沿径向非等截面环形叶栅的三维粘性流场，得到了诸如三维压力分布，总压损失分布以及十分清晰的二次流动图景等丰富的流场信息。

Using Hankel digital filter algorithm and inverse spine interpolation algorithm to simulate electromagnetic fields of the horizontal layers , we contrast the calculational Cagniard apparent resistivity with its results and field experimentation.

利用汉克尔数值滤波算法和逆样条插值算法对水平层状电磁场进行正演计算，并与计算的卡尼亚视电阻率的对比和野外试验结果表明：该方法的结果在远区等价卡尼亚电阻率，在近区和过渡带则明显地改善了卡尼亚电阻率的非波场区场畸变，从而能更好地接近基底的真电阻率，更形象地反映了地下介质的垂向电性变化。

In Chapter 2, a nonmonotone trust region method with a line search technique is presented. Unlike traditional trust region methods, our method does not restrict a monotonic decrease of the objective function value at each iteration, but only requires an average of the successive objective function values decreasing.

第二章，我们提出了一类带线搜索的非单调信赖域算法，与传统的信赖域方法不同的是：我们的算法不要求目标函数值在每一步都有充分下降，而是要求目标函数的连续平均值充分下降。

High precision format, unstructured dynamic mesh with a large displacement and multi-species gas flows were computationally expensive, the problem of resourceless and inefficient of single computer appeared. Parallel arithmetic based on PC-Cluster system for the oblique detonation wave flow and the muzzle flow include high speed projectile were discussed. The results proved that the rationality of parallel arithmetic provided a new method to simulate the complex chemical reaction flows. The present code represents a validated, efficient and versatile tool developed for the simulation of hypersonic multi-species chemical non-equilibrium flows.

高精度计算格式、化学反应源项的刚性和大位移的运动边界处理都给计算和存储带来了沉重的负担，单机资源不足和计算时间长的问题凸现，利用PC机和局域网资源建立分布存储式并行计算系统，并基于非结构动网格和分区算法开发了复杂化学反应流场数值模拟的并行计算程序，对高速飞行实验弹丸诱导的斜爆轰波流场和含有大位移动边界的膛口燃气射流场进行了并行模拟，有效地缩短了计算时间，扩展了计算规模，为复杂化学反应流数值模拟研究提供了新的手段。

This paper aims at detecting bursts of both monotonic and non-monotonic aggregates over multiple windows in data streams.

为了在数据流上检测多个滑动窗口上的单调聚集函数值和非单调聚集函数值的突变，提出了基于分形技术的构建单调搜索空间的突变检测算法。

At the same time, variational equations, their finite element formulations and numerical convolved integration algorithm of the model in current configuration usually called co-moving coordinate system are given.

基于非线性几何场论，建立了材料非局部连续模型、变分方程及相应的实时拖带系大变形有限元数值模型，设计了这一模型的数值卷积算法。

The above problems are studied in this thesis. First, the implicit NND scheme with mix flux splitting method proposed by Zhang Hanxin that is first order accurate in time and second order in space is modified. The modified scheme keeps the characteristics of fast convergence and is second order accurate both in time and space. It can be capable of simulating the unsteacly flow. Second, the topological method founded by Zhang Hanxin is improved to study the characteristics of vortex near the singular point on its axis and the cross streamlines on the longitudinal section passing the vortex axis. On the basis of topological results, a program which visualises numerical results is made out. It can help us analyse the characteristics of vortex motion.

本文对上述问题做了研究：第一，在数值模拟方面，借助于张涵信提出的NND算法和混合通量法，我们将他建立的时间为一阶、空间为二阶精度的快速隐式算法推广为时间和空间均为二阶精度的算法，这样做保留了原格式收敛快的特点，而且能适用于真实的非定常流态的计算；第二，将张涵信的拓扑分析方法加以推广，研究了涡轴附近及破裂点邻域内流场的空间特征，并以这些拓扑分析结果为指导，研制了一套显示计算结果的软件，这一软件能很好地帮助我们分析流场的计算结果和旋涡演变的特征。

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。