AH-FDTD方法在工程电磁耦合效应分析中的应用

电磁脉冲可通过对地下工程中的线缆和设备产生耦合,进而产生较大的瞬变电压和电流,导致电气系统出现故障或永久损坏.文中提出采用无条件稳定连带埃尔米特时域有限差分（associated Hermite FDTD,AH-FDTD）方法来分析场对地下工程的电磁耦合问题.建立了两种不同坑道模型（圆形和矩形）,采用AH-FDTD方法计算了坑道不同深度、不同被覆层岩土介质（色散和有耗）和不同斜入射角度情况下地下工程中场的分布,分析了不同坑道埋深、不同岩土介质和入射角度等条件下场对坑道工程耦合的影响.研究表明,场对地下坑道工程的耦合与坑道埋深、是否考虑岩土介质的色散性以及入射角度大小有关,而受坑道形状的影响相对较弱.所提AH-FDTD分析方法为防护工程电磁耦合效应研究提供了一种新的途径.     

预条件共轭梯度法在辐射和散射问题中的应用

用矩量法求解一些辐射和散射问题 ,如线天线辐射和线状体散射等问题时 ,可以产生一个 Toeplitz线性方程组 ,采用预条件共轭梯度法 (PCG)与快速富里叶变换 (FFT)的结合方法 (PCGFFT)来求解该方程组 ,其中预条件器采用 T.Chan的优化循环预条件器。使用 PCGFFT算法 ,可有效地节省内存 ,提高了计算速度。为说明其有效性 ,将 PCGFFT算法与 CGFFT算法以及 Levinson递推算法进行了对比。     

Application of Haar-wavelet-based multiresolution time-domainschemes to electromagnetic scattering problems

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite-difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation, which, in our case, consists of a pulsed plane wave. Also, we consider scattering in a half-space environment, with application to subsurface sensing. The results illustrate the advantage of the Haar MRTD method as compared with the classic FDTD, which consists of reduced memory and execution time requirements, without sacrificing accuracy     

Effective method for solving electromagnetic problems

The authors discuss a neural network model for solving electromagnetic problems which can be represented as combinational optimisation problems, with cost functions as the network energy. Solutions correspond to the minimum of energy. An example is given to illustrate the method     

Three-dimensional finite-element method for solving electromagnetic problems

A 3-dimensional numerical method of determining the vector fields within a closed lossless electromagnetic system is described. The method is used to find the dominant-mode resonant frequencies for two cases of a rectangular cavity partially loaded with dielectric.     

Application of the Fourier-grid method to guided-wave problems

A method recently developed for solving the Schrodinger equation is applied to dielectric waveguides. The technique, which is extremely simple to implement, involves representing the differential operator in the scalar Helmholtz equation on a grid of discrete points in coordinate space, and then diagonalizing the resulting matrix to reveal the propagation constants and field patterns of the guided modes. The square of the transverse index profile is specified directly as a diagonal matrix in coordinate space, while the matrix for the transverse Laplacian is obtained through the Fourier relationship between its diagonal form in momentum space and the equivalent representation in coordinate space. The accuracy and computational performance of this procedure is assessed for one- and two-dimensional transverse profiles. Modal refractive indices and fields computed by the grid method are found to agree well with those derived by means of other techniques     

Topology-finite-element method for solving electromagnetic field problems

The topology-finite-element method has been proposed for solving electromagnetic field problems. This method is characterised by a higher degree of simplicity and standardisation in comparison with the finite-element method. On the other hand, the mathematical model derived by this method is proved to be simple and of evident geometric and physical significance as well, thus creating favourable conditions for making optimal designs in engineering science.     

基于阻尼最小二乘法的瞬变电磁反演算法研究

反演问题是根据实际测量的地层电磁场数据定性或者定量解释出地球内部的结构的过程。反演与正演是相互对应的,反演模型不仅能检测正演模型的准确性和可靠性,也能为地质解释提供依据,而反演也是瞬变电磁检测的难点与重点之一。本文详细介绍了瞬变电磁检测的反演原理,采用阻尼最小二乘法优化逼近正演结果的算法进行瞬变电磁反演的计算,并通过软件对实际地层数据进行反演,得到不同电阻率初值的地层反演结果。反演结果表明该方法切实可行,误差较小。     

Application of the unimoment method to electromagnetic scattering of dielectric cylinders

The unimoment method is applied to calculate the scattered fields of dielectric cylinders of arbitrary cross section or of inhomogeneous material. The basic technique of the method is the use of the finite element methods inside a mathematical circle, which encloses the inhomogeneous body. The fields outside are expanded in the usual cylindrical harmonics. The interior and exterior problems are then coupled at the circle. The versatility is increased greatly by introducing the method of "inhomogeneous element." The advantage of the proposed method is the simplicity and efficiency in programming. The validity of the computer program has been verified by comparing results with calculations from other methods for i) an off-centered circular cylinder, ii) two circular cylinders, and iii) a circular cylindrical shell.     

Finite-element solution to electromagnetic scattering problems bymeans of the Robin boundary condition iteration method

A new numerical method, called the Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods     

Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems

A three-dimensional (3-D) multiresolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yielding update equations involving a small number of proximate field components. A detailed analysis is presented on algorithm implementation, with example numerical results compared to data computed via the conventional finite-difference time-domain (FDTD) method. It is demonstrated that for 3-D scattering problems the CDF-based MRTD often provides significant computational savings (in computer memory and run time) relative to FDTD, while retaining numerical accuracy.     

Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems

An iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems, in an attempt to characterize the typical rate of convergence of that method. It is found that this rate depends on the cell density per wavelength used in the discretization, the presence of symmetries in the solution, and the degree to which mixed cell sizes are used in the models. Assuming cell densities used in the discretization are in the range of ten per linear wavelength, the iterative algorithm typically requiresN/4toN/2steps to converge to necessary accuracy, whereNis the order of the matrix under consideration.     

分段积分共形算法在电磁散射问题中的应用

提出一种分段积分共形时域有限差分算法(PI-CFDTD),用于计算电磁散射问题。首先采用邻近网格电场场量插值表示变形网格中沿线电场场量,再以分段积分代替传统电场沿线积分求解,减小了阶梯误差,提高了电场环路积分的计算精度。推导出两种不同类型变形网格的电场环路积分公式,并对PI-CFDTD算法的稳定性进行研究,归纳得到应用原则。以金属方形平板和金属圆形平板作为算例进行验证,通过与传统时域有限差分法(FDTD)、传统共形时域有限差分法(CFDTD)以及矩量法(MoM)进行比较,表明PI-CFDTD计算精度更高。     

Multigrid transmission-line modelling method for solving electromagnetic field problems

The development of a novel approach to solve electromagnetic problems in three dimensions is presented. The method described as the 'multigrid TLM method' uses different grid sizes to model space thus allowing the modelling of small features using a fine mesh of grid points, whereas the rest of space is modelled using a coarse mesh. The advantage of this method is that it offers simultaneously very high space resolution and modest computer storage and run-time requirements. The basis of the method is described briefly, together with typical results and conclusions.<>     

Solution to some electromagnetic problems using fast Fourier transform with conjugate gradient method

Using the fast Fourier transform (FFT) to compute the convolution integrals that appear in the conjugate-gradient method (CGM), an efficient numerical procedure to solve electromagnetic problems is obtained. In comparison with the method of moments (MM), the proposed FFT-CGM avoids the storage of large matrices and reduces the computer time by orders of magnitude.     

Choices of expansion and testing functions for the method ofmoments applied to a class of electromagnetic problems

It is well known that the choice of expansion and testing functions plays an important role in determining the rate of convergence of the integrals associated with the moment method matrix, and that an improper choice can lead to erroneous results. This convergence issue is critically examined, and to criteria for the choice of these expansion and testing functions are provided. The question of whether these functions need to satisfy the Holder condition is also investigated, and the convergence behavior of the integrals involved in the spatial- and spectral-domain moment method is discussed for some representative expansion and testing functions     

Solving electromagnetic field problems using a multiple gridtransmission-line modeling method

A multiple grid technique for solving electromagnetic field problems using the transmission-line modeling (TLM) method is described. The ideal conversion conditions across the interface between fine and coarse mesh regions are described and the implications of making the approximations needed for a practical implementation are discussed. Simulations are presented showing the accuracy of the method and its benefits in terms of reduced storage and run-time     

Application of stochastic second-degree method to electromagnetic scattering from randomly rough surfaces

Application of a stochastic second-degree method in combination with the banded matrix canonical grid (BMIA/CAG) method for two- dimensional electromagnetic scattering from PEC randomly rough surfaces is presented. This method can improve convergence while preserving the computational attractiveness of the BMIA/CAG method. Numerical examples illustrate the effectiveness of the proposed method.     

复合网格法在电磁散射问题中的应用研究

复合网格方法采用区域分解算法的思想,将计算区域分为粗网格与细网格两个区域.在电磁散射问题中,细网格区域包含了微细结构的电磁散射信息.利用连接边界条件,将粗网格计算结果和细网格计算结果分步进行计算,从而得到包含有微细结构的电磁散射信息.该计算方法可以减少此类计算问题的计算量,所得结果与全部区域进行细网格划分的结果进行了比较,两种结果复合很好.     

电磁响应的时、频域同时外推法

将散射体在高斯脉冲平面波激励下感应电流的时域响应展开为连带Hermite级数的叠加，利用傅立叶变换和连带Hermite函数的自反性，得到与时域响应形式类似的感应电流的频域响应。根据时域解与频域解的对应关系，利用感应电流的早时响应和低频响应，可确定展开式的未知系数，从而同时获得了时域和频域和完全响应。