基于边界元法的微结构光波导模场分布研究

本文基于加权余量法,阐述了利用边界元法求解矢量亥姆霍兹方程的数学基础-亥姆霍兹方程的边界积分方程;并推导了数值求解该边界积分方程的方法;利用推导结果,编写计算机程序分析了圆光波导的模式场分布情况。实验结果表明,该方法可以在较低方程组阶数,较少输入数据量的前提下准确地分析微结构光波导内模式场的分布情况。     

环型激光束空间传输的数值模拟

基于Maxwell方程组的经舆理论,对于腔的菲涅耳数不满足远远大于1的条件时的光束传播问题,利用衍射积分方程理论进行求解．根据菲涅耳-基尔霍夫衍射积分方程建立数值模型,采用matlab数值模拟的方法,对环型激光束传输方向的近场及远场强度的空间分布进行了分析．     

二维扩散方程边界元解法中的四重奇异积分计算

对二维热传导方程的Dirichlet初边值问题,采用带时间变量的基本解,利用基于单层位势的间接边界积分方程及其等价的Galerkin变分形式求解,该方法涉及到与时空相关的四重奇异积分的计算.在采用常单元离散的情况下,推导了具体实施数值计算所需的积分公式,完成了数值实验,验证了该方法的有效性和可行性.     

求解时域电场积分方程的偏置网格有限差分法

细线、薄板状良导体的时域散射特性可由“全切向”时域电场积分方程（TDEFIE）描述。本文采用偏置网格的有限差分方法数值求解“全切向”TDEFIE。这种网格充分利用物体的几何、物理特性,数值实现简便。利用这种方法,本文研究了电磁辐射、散射的三个经典问题,同时分析了方法本身的数值稳定性。数值结果表明,该方法求解时域电场积分方程有效。     

精确稳定求解时域电场积分方程的一种新方法

时域电场、磁场和混合场积分方程已被广泛用来分析散射体的时域散射响应.基于适当的空间积分方法和隐式的时间步进算(MOT)法在求解时域磁场和混合场积分方程时总是稳定的,然而在求解TDEFIE时则是不稳定的.在本文中,时域电场积分方程的非奇异性积分采用标准的高斯求积法来计算;而利用参数坐标变换和极坐标变换将其奇异性积分转换成为可以分区域精确快速计算的非奇异性积分.通过数值实验表明,利用该方法可以非常精确稳定地求解时域电场积分方程,即使是在时间迭代后期也不必采用任何求平均的过程;另外,该方法可以用于任意时间基函数并可以推广到高阶空间基函数的情形.     

基于高阶叠层矢量基函数的时域电磁场 积分方程方法

本文将准正交高阶叠层矢量基函数用于时域电磁场积分方程(TDIE),求解了三维金属目标的时域电磁散射问题.准正交高阶叠层矢量基函数定义在曲面四边形单元上,并且不要求网格为规范网格,给复杂目标的几何建模和电磁建模带来很大方便.在空间上利用伽略金方法、时间上采用点匹配法求解时域电磁场积分方程,并采用隐式时间步进算法,数值计算结果表明了该方法求解时域积分方程的精确性、高效性与稳定性.     

利用高阶矢量基函数求解时域磁场积分方程

本文利用一种新的高阶矢量基函数求解了三维时域磁场积分方程,该基函数定义在一个曲边三角形贴片上并用拉格朗日插值多项式来表示每一个贴片内的未知电流密度.该基函数的实质就是将拉格朗日插值多项式的插值点选为高斯积分结点,极大地简化和加快了时域积分方程矩量法的繁琐的时间和空间积分运算;另外,该基函数不要求网格为规范网格,给复杂目标的网格剖分带来很大方便.在空间上利用点匹配方法求解了时域磁场积分方程,数值计算结果表明了该方法求解时域积分方程的精确性和高效性.     

基于TDOA移动定位中的约束加权最小二乘算法

自E-911定位需求顽布以来，移动台定位技术在国内外受到了高度的重视和深入研究。本文主要对无线定位中基于TDOA的一种约束加权最小二来算法进行了研究。该算法通过引用一个中间变量重组非线性方程组为线性方程组，然后利用加权最小二来算法对该方程组进行求解，得到移动台的第一次位置估计值，根据得到的估计位置以及他们之间的内在联系，并引入拉格朗日来数因子重新建立一个方程来对第一次估计进行修正，求解出符合条件的拉格朗日乘数因子，从而得到第二次位置估计值。仿真结果表明在一定的噪声环境中约束加权最小二来算法能够达到克拉美罗下限，取得了较好的定位效果。     

半解析/半数值OLED器件黑点扩散模型的Matlab分析计算

介绍了求解OLED器件黑点扩散模型的一种半解析/半数值计算方法.该方法综合利用Matlab提供的求解常微分方程、矩阵行列式、数值积分等函数,可使模型分析计算的工作量大为减少.给出了杂质浓度的计算公式,对于其中涉及的积分方程,基于数值逼近原理,采用多项式拟合函数近似求解.该方法具有编程简单、使用方便、实用性强等特点.     

高效求解任意非常规目标电磁散射的修正电场积分方程方法

本文研究了一种可以高效求解任意非常规目标电磁散射的修正电场积分方程方法.借助磁场积分方程主值项的提取,加入到传统电场积分方程中,将传统的一次迭代求解过程转变成逐渐逼近真解的内外两层迭代.其外层迭代不断刷新电流,最终得到精确解.加入磁场主值项的修正电场积分方程显著降低了条件数,同时保留了原电场积分方程普适性强,可用于处理任意非常规目标的优点.对于每一外层迭代步中电流的求解,本文采用了加速矩阵矢量相乘的多层快速非均匀平面波算法,形成高效的内层迭代求解.数值结果表明,该方法在保证精度的同时,可以显著降低问题的求解时间.     

Propagation and coupling properties of integrated opticalwaveguides-an integral equation formulation

The propagation and coupling properties of integrated optical waveguides are analyzed by means of the electric field integral equation approach. The kernel of the integral equation is the Green's function of a two-layered medium. The Galerkin's method is then employed to solve the integral equation numerically. The set of basis and test functions consists of entire domain plane wave functions. Fast convergence and superior accuracy are the advantages of the chosen set of basis and test functions. The method is used to compute the propagation and coupling properties of several structures. Very good agreement is observed with previously published results. Field distributions of several coupled mode structures, such as the symmetrical and asymmetrical coupler are also investigated and presented. Finally, the same method is used to produce the field distribution of waveguides having more complex cross section like the trapezoidal waveguide     

Near-field analysis of spherical loop arrays

In a recent paper (see ibid., vol.42, p473-7, April 1994), the authors presented the development of an algorithm for the reconstruction of element currents of a spherical loop array given the far-field pattern data in an azimuthal plane, and demonstrated the validity of the method with several computational examples. In this letter, it is shown that the same algorithm can be applied to the reconstruction of the spherical loop-array currents from the near-field data by application of spherical wave expansion of the electric field integral of the array. The main feature of the reconstruction algorithm is that the array currents are obtained recursively through the solution of a triangular equation set     

Full wave analysis of microstrip floating line structures bywavelet expansion method

A full wave analysis of microstrip floating line structures by wavelet expansion method is presented. The surface integral equation developed from a dyadic Green's function is solved by Galerkin's method, with the integral kernel and the unknown current expanded in terms of orthogonal wavelets. Using the orthonormal wavelets (and scaling functions) with compact support as basis functions and weighting functions, the integral equation is converted into a set of linear algebraic equations, with the matrices nearly diagonal or block-diagonal due to the localization, orthogonality, and cancellation properties of the orthogonal wavelets. Limitations inherited in the traditional orthogonal basis systems are released: The problem-dependent normal modes have been replaced by the problem-independent wavelets, preserving the orthogonality; the trade-off between orthogonality and continuity (e.g. subsectional basis functions including pulse functions, roof-top functions, piecewise sinusoidal functions, etc.) is well balanced by the orthogonal wavelets. Numerical results are compared with measurements and previous published data with good agreement     

Calcul des réponses impulsionnelles de cibles acoustiquement réfléchissantes

From the wave equation and the use of boundary conditions of the problem we have developped an integral equation which is time dependant. The particular form of this integral equation is well suited to a numerical approximation method which gives the solution as a single boundary layer. If one knows this boundary layer for all space and for all time, one can calculate the spacetime response of the target under investigation. The method is a very general one and can be applied to targets of arbitrary shape. To check the efficiency of the algorithm a computation has been done in the particular case of a perfectly reflecting sphere. Results are in good agreement with classical ones reported in the littérature.     

Radar cross section of arbitrarily shaped bodies of revolution

The radar cross section (RCS) of an arbitrarily shaped, homogeneous dielectric body of revolution (BOR) is evaluated by the surface integral equation (SIE) formulation and the method of moments. Method accuracy is verified by the good agreement with the exact solutions for the RCS of a dielectric sphere. To demonstrate the advantages of this method, the RCS for a complex BOR model of human torso is computed with a nonaxially incident plane wave. Seven Fourier modes are considered in the computation. The SIE and approximate integral equation (AIE) formulations are next given for the RCS evaluation of a composite dielectric and conducting BOR. For the cases considered, both formulations give the same surface currents and RCS results. However, significant savings in computer storage and CPU time are realized for the AIE approach, since only one current (electric or magnetic) need be determined for RCS evaluation     

Numerical solution of the problem of diffraction of electromagnetic waves by nonplanar screens of complex geometric shapes by means of a subhierarchic method

The problem of diffraction of an electromagnetic wave by a nonplanar screen of a complex geometric shape located in free space is considered. The problem is reduced to an integral equation. A numerical method is proposed and realized with the use of rooftop functions for the solution of the integral equation. A subhierarchic method is applied for the solution of the integral equation. Numerical results are presented.     

基于双感应测井仪低数据量的反演方法研究

将一种迭代方法和双共轭梯度法用于实际工程中常用的双感应测井仪（DIT）的反演和剖面成象。基于目标区内、外电场积分方程,建立DIT的反演积分方程,利用MoM将积分方程高散为矩阵方程。在每次反演迭代过程中,用数值模式匹配法（NMM）求解DIT的感应电动势和格林函数。文中利用沿井轴的DIT不完备的低信息量对地层剖面进行反演,数值模拟结果表明该迭代方法的实际工程应用的潜力。     

用时域积分方程法计算介质目标的电磁散射

本文应用时域积分方程法计算介质目标的散射场，并以球体和带球帽的圆柱体为例给出了沿轴向入射平面波的电磁散射结果，与实际测试结果非常一致，值得指出的是，虽然本文给出的介质目标具有平面对称性，但该方法适用于任意形状的目标。     

预估城镇小区电波传播损耗的一种三维抛物方程算法

为城镇小区电波传播问题建立了一种三维抛物方程模型,并且用二维分部傅立叶变换方法求解。计算了几种不同地形上建筑物障碍分布的小区电波传播衰减因子,和UTD理论及数值积分方法计算出的结果吻合得比较好,从而验证该模型的有效性,同时也说明了三维抛物方程模型能更准确地反映出小区建筑物宽度对场的绕射作用,为城镇小区电波传播问题的估算提供了一种更为准确的算法模型。     

On the use of spatio-temporal wavelet expansions for transient analysis of wire antennas and scatterers

To analyze a wire antenna excited by a time varying voltage source or a wire scatterer excitated by transient electromagnetic incident wave, the problem is formulated in terms of a time-domain integral equation for the induced current. To solve the integral equation, we reduce it to matrix equation via the method of moments using the known-to-be-stable implicit scheme. However, rather than directly constructing and solving the relatively large matrix equation, we propose an iterative procedure which allows us to gradually obtain a solution of refined accuracy both everywhere and simultaneously at any time instance. To render this procedure rapidly converging, we use a basis of spatio-temporal wavelet functions. This basis facilitates a good approximation of the induced current using far less basis functions than would be needed if other expansions, such as standard-pulse or Fourier basis functions were chosen. The use of this basis further enables the iterative procedure to increase the temporal and spatial resolutions where required without unnecessarily affecting their levels elsewhere.