数值算法

In addition, the return mapping algorithm is built in negative normal convex cone of violated constraints of level sets to conveniently give an initial structure with multi-constraints, multi-materials and non-design domains.

在这些研究的基础上，提出了适用于一般目标函数、多材料、多约束和多载荷工况的结构拓扑优化的水平集算法4.1，并给出了刚性结构、柔性机构和复合材料微结构设计算法5.1、6.1和7.1，以及大量的数值算例。

The steepest descent method was applied in optimization to solve the quadratic matrix equation,and a new algorithm was given.

结合优化理论中最速下降法思想，给出一种新的算法解二次矩阵方程，并列出几个数值例子说明算法是可行的。

To get high numerical stability and computational efficiency, U-D factorization-based DFP and BFGS algorithms are developed.

该算法解决了H阵的正定性问题，保证了算法的数值稳定性，并大大提高了计算效率。

Firstly, illustrate the fundamentals (differential-integral optimizing theory) of the category of algorithms briefly in the sight of differential and integral calculus. Then two examples of the category of algorithms are listed.

首先从函数逼近的角度论述了数值积分与全局最优化的关系，随后从微积分的基本原理和定积分的定义出发对该类算法的几何意义和数学基础作了简要论述；在此基础上给出了该类算法的几个具体实现。

Three solution algorithms for classical transportation continuous/discrete/ mixed network design problems are designed based on particle swarm optimization approach, in which the continuous NDP is studied in detail, discrete and mixed NDP are only described the frameworks of the solution algorithms.2. Generally, road capacity constraints must be added to the lower level problem of classical discrete NDPs bilevel programming model in order to avoid traffic assignment on candidate roads.

本论文研究工作主要有如下几个方面：(1)基于粒子群优化思想设计了求解传统的城市道路交通网络设计问题的算法，其中详细研究了连续网络设计问题，并用两个网络例子进行了数值实验；并给出了离散网络设计问题和混合网络设计问题的求解算法思路和主要步骤。

A parallel split iteration algorithm for MIMD distributivity memory cluster on solving linear coefficient matrices is established in chapter three. Convergence is proved when the coefficient matrix is Hermite positive definite matrix or M-matrix. Discussing convergence range of parameter T . In the end, examples have been implemented on HPrx2600 cluster, and the data verify that the algorithm has favorable astringency and parallelism.

研究了一种适合于MIMD分布式存储并行机的交替方向法，理论上证明了在系数矩阵为Hermite正定矩阵和M-矩阵时算法的收敛性，讨论了参数τ的收敛范围，最后在HPrx2600集群上进行数值试验，结果表明此算法有良好的收敛性与并行性。

Within this algorithm, Alopex algorithm is used to Elitist maintained Genetic Algorithm.

数值计算结果表明该算法优于求解函数优化的EGA和Alopex算法。

When the quasi-solution existence theorem of the equation has been proved,the algorithm getting quasi- numerical solution by computer is presented.

在方程的适定性和拟解的存在性都已得到证明的情况下，提出了能通过计算机得到近似数值解的算法，讨论了算法的可行性并进行了误差估计。

The nonsmooth damped Newton method is given based on the definitions of the generalized derivative.

数值试验结果也表明该算法同光滑化算法同样有效。

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。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。