电磁场

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。

The inverse radius vector transform is applied in this paper to change the boundless space into a bounded domain,so that the finite element method can be used in computing electromagnetic fields with open boundaries.

目前，在电磁场数值分析中，有限元法得到了广泛的应用，但一般都认为有限元法适用于有界空间中的电磁场问题，这是因为对于无界空间中的电磁场问题，方法的直接应用存在着一定的困难。

In 2D eddy current field computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by the GMT, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁场分析中存在一种无穷级数收敛，且有一定普遍性的解析解。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

Firstly, according to electromagnetic field theory, the 2-dimensional (2-D) mathematical model of a three phase squirrel-cage Y802-2 induction motor is developed. Then general equations can be deduced from finite element discrete and functional analysis. The motor's 2D solving region of electromagnetic field is given based on the boundary conditions and assumption conditions of the squirrel-cage induction motor. Through finite element mothod and inner–outer convergence method, magnetic field distributions and magnetic forces of bars can be calculated in following rotor conditions: health rotor, one single broken bar, two adjacent broken bars, two broken bars with one good interval, two broken bars with two good interval and four adjacent broken bars.

本文首先根据电磁场理论建立Y802-2型三相笼型感应电动机二维电磁场的数学模型，并对其进行了有限元离散以及泛函分析，推导出总体方程；在基本假设和边界条件基础上，给出笼型感应电动机二维电磁场的求解区域，然后应用有限元并结合内外双收敛方法，对样机稳态运行进行数值计算，得出电机在转子完好、一根导条断裂、连续两根导条断裂、间隔一根两根导条断裂、间隔两根两根导条断裂及连续四根导条断裂六种情况下的磁场分布和导条所受电磁力的变化情况。

First, based upon the fields in the single cavities, open and short modes are constructed, whose coupling holes on disks are shorted magnetically and electrically respectively. Second, the whole field in the chain is expanded with the short and open modes. With the Galerkin method and the second vector Green theorem, it is possible to describe the physics problem by a simple general eigenvalue matrix equation. Here, the dispersion curves in periodical structures are available.

它首先利用有限元等方法计算各加速单腔中的电磁场，根据一定规则构造成所需的开模和闭模，然后把整个长腔链加速结构中的场用这些开模和闭模展开，再利用伽略金方法和第二矢量格林定理进行数学变换，考虑各模式在加速腔壁和腔间耦合孔处的边界条件后，就能把加速结构中电磁场用数学上的广义本征值矩阵问题描述，从而能够得到所求的色散曲线和电磁场形态。

The harmonic field of electric dipole source on the uniform earth surface is converted into transient field by inverse Laplace transform,and the Bz/ t transient curve is calculated.The Hz transient curves on the stratified earth surface are obtained from cosine transform calculated by broken line approximation.

由逆拉普拉斯变换将均匀大地面上的电偶极子源谐变电磁场转换为瞬变电磁场，并计算出Bzt瞬态曲线；对分层大地面上的瞬变电磁场，采用折线逼近法计算余弦变换得出Hz瞬态曲线。

The EM field of arbitrary point in an irregular loop can be considered as the sum of the EM field of many circle loops in the irregular loop at the point. Therefore the authors may obtain the EM field of the irregular loop as long as the authors work out the EM field of each of the circle loops.

不规则回线内任一点的电磁场可以看成是其内部多个圆形回线在该点的电磁场之和，因此，只要求出不规则回线内各个圆形回线在该点的电磁场，将它们叠加就可得出不规则回线在该点的电磁场。

For this purpose, the compactly supported radial basis function and the moving least squares approximation based ones are integrated into the aforementioned two global optimizers. As a result, two novel hybrid algorithms are introduced.

其次，为解决电磁场逆问题分析、计算中由于随机类优化算法需进行数以千计次电磁场的数值分析，以致计算时间和计算量难以满足工程分析实际要求的难题，本文将表面响应模型法引入电磁场逆问题的求解，研究了基于紧支径向基函数和基于移动最小二乘法的两种表面响应模型，并将其分别与改进的遗传算法和粒子群算法相结合，提出两种不同的混合快速全局优化算法。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。