数值分析

This thesis contributed to the comprehensive study of the Finite-Difference Time-Domain method and its application to the numerical computation of radiated electromagnetic fields in switched mode power supplies. The work includes mainly three parts: the study on the performance of PML absorbing boundary condition applied to pseudo low frequency electromagnetic problems; the validation of the FDTD method with PML absorbing boundary conditions and the corresponding computer software based on the numerical study of the electromagnetic field of an electric dipole antenna, and its application to the numerical computation of radiated electromagnetic fields in switched mode power supplies; the development of an improved alternating direction implicit finite-difference time-domain method.

在综合前人工作基础上，本文对时域有限差分法及其在开关电源辐射电磁场数值计算中的应用进行了系统的分析和研究，其核心内容包括：伪低频电磁场数值计算中PML吸收边界条件性能的研究；基于基准问题—电偶极子天线三维辐射电磁场，验证了本文构造的基于PML吸收边界条件的三维FDTD法及其计算软件，并应用于高频开关电源辐射电磁场的数值分析；提出了一种改进的交替方向隐格式时域有限差分法。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

The main results can beexpressed as follows:(1)Based on πtheory, some affected factors about wave forces are given, and therelation between affected factors and wave forces is analysised by experimentalresults.(2) The distribution of wave press at representative time and reflection nature aregiven and their variety charactes are discussed by experimental results.(3)By comparing the wave forces of quarter-circular breakwater and semi-circularbreakwater under the same wave conditions,some approximately wave forcesexpressions of quarter-circular breakwater are given.(4)Based on VOF method to trace water free surface,solve numerical value ofRANS equation,and get the distributions of flow field and wave press ofquarter-circular breakwater at the same time during one period,the mechanism ofwave force is also discussed elementarily.(5) Based on the result that RANS equation of numerical simulation agree wellwith experimental results,a new approach to study hydraulic natures of quarter-circular breakwater is provided.

其主要结论如下：一、通过π定理，确定影响波浪力的无因次参变量，根据试验结果对其影响因素进行分析；二、基于模型试验，给出典型时刻圆弧面防波堤的同步波压分布和反射特性，讨论它们的变化特点；三、通过相同条件下圆弧面防波堤与半圆型防波堤两种堤型试验波浪力的比较，给出了圆弧面防波堤波浪力的近似方法；四、利用VOF法追踪自由水面，数值求解RANS方程，得到圆弧堤堤体周围的流场和压力场，初步分析了速度涡流与压力场的相互影响；五、对比数值分析与试验结果，探讨数值方法研究圆弧面防波堤水力特性的可行性，提供新的研究途径

The primary studying works and characteristics:1 To summarize reinforcing theory of cement mixing pile composite foundation2 To analyze the primary mechanics characters and changing rules of cement mixing pile, based on analysis of test data both indoor and outdoor.3 To discuss siding frictional resistance, ending resistance, ultimate bearing capacity of simple mixing pile and effectiveness factor of grouped piles, loading ratio of soil between piles under cushion cap of grouped piles and stress ratio of pile and soil and so on, and use many computation method and experimentation method to ensure bearing capacity of mixing piles composite foundation.4 To point out and analyze eight sides flaws and problems of the bearing capacity calculation method of mixing pile compositefoundation which ensured by national and normative method/ formula.5 To apply test results of loading tests and a few settlement observation data, use gray theory to predicate ultimate bearing capacity of deep mixing piles, actual example demonstrate engaging between theoretical predicted value and actual value.6 To apply groovy layerwise summation method to discuss entity piles method, double foundation method, equivalent layerwise summation method and consolidation theoretical method and so on, especially by combination of engineering example, use FEM to calculate or discuss the settlement and changing rules of composite foundation.7 To discuss problems of critical length of composite foundation by combination of engineering example and numerical analysis method, and analyze the contrast of critical length between simple pile load and most area load of composite foundation, not only critical length of composite foundation is relative to modulus ratio between piles and soil, but also upside load distribution area of composite foundation.

主要的研究工作与特色为：(1)总结了水泥搅拌桩复合地基的加固原理；(2)在对室内外试验资料进行统计分析的基础上，系统分析了搅拌桩水泥土的主要力学特性及其变化规律；(3)探讨了搅拌单桩的侧摩阻力、端阻力、极限承载力及群桩效率系数、群桩承台下桩间土荷载分担比及桩土应力比等，提出用多种计算方法并结合试验方法来综合确定搅拌桩复合地基的承载力；(4)明确指出和分析了按国家有关规范的方法确定搅拌桩复合地基承载力所存在的八个方面的缺陷与问题；(5)利用过去没有加载至破坏阶段的载荷试验成果和较少的沉降观测数据，尝试了用灰色理论预测深层搅拌桩的极限承载力，实例表明理论预测值与实测值吻合较好；(6)在常规分层总和法的基础上，探讨了复合地基沉降计算的实体墩基法、双层地基法、等效作用分层总和法、固结理论法等，特别是结合工程实例，用有限元数值计算等方法计算和讨论了搅拌桩复合地基的沉降及其变化规律；(7)结合工程实例，用数值分析方法探讨了复合地基临界桩长的问题，指出和分析了单桩荷载下的临界桩长与复合地基大面积荷载下的临界桩长存在很大的差别，复合地基的临界桩长不仅与桩土模量比有关，而且与复合地基上部荷载分布面积有关。

Numerical Analysis - Dave Rusin; The Mathematical Atlas 数值分析----Dave

本页为短篇论文的集合，用来提供一个对数值分析的介绍。

Numerical Analysis - Dave Rusin; The Mathematical Atlas -数值分析----Dave Rusin

数学文集。本页为短篇论文的集合，用来提供一个对数值分析的介绍。

Main research works are as follows:(1) Numerical simulation of turbulent flow and combustion in power plant furnace (2) Numerical simulation of fire spread and crown fire in forest fire behave (3) Numerical simulation of burning process of large space building (4) Numerical simulation of three-dimensional fluid flow of satellite cabin in microgravity environment (5) Numerical simulation of burning process of multi-rooms It shows that the ability of FAC3 and FZ code is strong and the code is widely used for practical problems.

研究工作主要涉及以下几个方面：（1）电站煤粉锅炉流场的数值分析（2）林火行为中火蔓延和树冠火等特性的数值研究（3）大空间建筑火灾烟气流动过程的数值分析（4）微重力条件下卫星密封舱内部流场的数值分析（5）多室火灾过程的数值分析研究工作表明，FAC3和FZ程序的功能较强，通用性较好，可对多种热过程现象进行数值模拟，在一定程度上讲，即可用于科学研究，又可用于实际工程问题，并具有广泛的应用前景和推广价值。

This enriched and developed the basic thought of numerical theory, resolved the bottleneck problem that astricts the development of numerical value analysis method, open up a new field for the geomechanic engineering application of 3-D network and numerical value analysis method, it's an available and essential attempt, it's also a necessary trend of numeric times development.

10通过岩体三维节理网络模拟，建立岩体结构的概化模型，基于数值法对岩体进行大量的&数值模拟试验&，获取岩体变形参数，丰富并拓展了数值模拟理论的基本思想，解决了选择岩体参数这一束缚数值分析方法发展的瓶颈问题，为数值分析方法和三维节理网络在岩土工程实践中的应用拓展了一片新的天地，是一种有益而且非常必要的尝试，也是数字时代发展的必然趋势，具有一定的理论意义和应用价值。

Based on them, distribution laws of subgrade temperature field under fluctuant boundary temperature cycle conditions are analyzed, and different ratios of slope for general subgrade and different status when there are or not banquettes are compared by laboratory simulation and numerical analysis; thermal insulation and cooling effect of thermal insulation slab, broken stone and non-power heat pipes is respectively investigated under the trend of elevated temperature by numerical analysis, laws of subgrade deformation are predicted under the trend of elevated temperature and influences of subgrade thaw settlement on pavement stress are studies by numerical computation for observation data of representative road sections selected.

为研究青藏公路冻土病害处治对策，从青藏公路2002年～2004年冻土病害整治工程实际出发，在系统分析研究青藏公路病害及发生机理的基础上，运用室内模拟试验、数值分析方法，依托处治冻土病害路段实际使用的隔热板路基、碎石路基、无动力热棒路基等进行现场试验，分析边界温度周期波动条件下的路基温度场分布规律，同时进行一般路基不同边坡坡率的对比研究及有无护坡道的对比研究；运用数值分析方法，对气温升高趋势下隔热板、碎石、无动力热棒的隔热降温效果进行了研究；选择代表性路段观测资料，运用数值计算的方法，进行升温趋势下的路基变形预测，研究路基融沉变形对路面应力的影响。

Professor L N Trefethen, Numerical Analysis - Balliol College, Oxford University, UK - L N Trefethen教授,数值分析----牛津大学Balliol

学院。链接到牛津大学数值分析研究团体出版的图书与近期发表的论文。

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。