Analysis of Low-Frequency Electromagnetic Transients by an Extended Time-Domain Adaptive Integral Method

A stable and fast marching-on-in-time based integral-equation solver for analyzing low-frequency electromagnetic transients is presented. Stability and computational efficiency are achieved by using a frequency-normalized and diagonally balanced loop-tree decomposition scheme in concert with a novel fast Fourier transform (FFT)-based acceleration scheme. The proposed algorithm extends the time-domain adaptive integral method (TD-AIM) into the low-frequency regime by accelerating the computations of not only (discrete) "delayed" interactions due to fields observed one or more time steps after being generated but also "instantaneous" interactions due to fields observed less than one time step after being launched. This is realized by augmenting the four-dimensional blocked space-time FFTs in the TD-AIM recipe with three-dimensional space-only FFTs. Application of the extended TD-AIM accelerated integral-equation solver to the analysis of package geometries demonstrates its accuracy, stability, and efficiency.     

运动薄板的平均边界条件

考虑到利用精确边界条件处理电磁屏蔽问题的复杂性,为简化电磁屏蔽边值问题的分析与计算,该文在平均边界条件的基础上给出了运动薄板电磁屏蔽边值问题求解的一种新的近似方法。通过编程上机计算,得到了运动薄板近似传输系数的值,经与精确边界条件下运动薄板准确传输系数的值比较,发现两种结果符合得很好。这表明本文中的方法不仅是简便易行的,且可以足够准确地描述薄板两侧电磁场的分布情况。     

Novel FDTD simulation method using multiple-analysis-space for electromagnetic far field

Wide-band undesired electromagnetic noise near electronic systems, which includes small noise source like the printed circuit board (PCB), is a current problem in the field of electromagnetic interference. However, the estimation method for the electromagnetic noise near a system under test has not been established. This paper proposes a newly developed estimation method of the electromagnetic noise for a wide area, from near to far field, using the finite difference time-domain (FDTD) method. The proposed FDTD simulation method is an estimation technique for near to far field with multiple analysis spaces (MAS). The MAS has an internal analysis space (IAS) and an external analysis space (EAS). The analysis near a radiation source can be calculated in the IAS. The EAS is the outside space from IAS, which is for calculation of the far field. It is expected that the proposed FDTD method by MAS (FDTD-MAS) decrease in the calculation cost in terms of computational time and memory costs, especially for estimation of radiation from PCB. The principle procedure of the FDTD-MAS method is described in the first part of this paper. As example of advantages of the calculation and confirmation of the calculation accuracy, the electric field distributions radiated from a 1-GHz half-wavelength dipole antenna in an IAS of 0.3/spl times/0.3 m/sup 2/ area and an EAS of 7/spl times/7 m/sup 2/ area are used as examples. When the cell size ratio of IAS to EAS is changed from 6 to 20, the FDTD and theoretical values show good agreement. It is indicated that the FDTD-MAS simulation method is one of the most powerful tools for the estimation of electromagnetic noise from near field to far field from small and thin source.     

Efficient time-domain and frequency-domain finite-element solutionof Maxwell's equations using spectral Lanczos decomposition method

An efficient three-dimensional solver for the solution of the electromagnetic fields in both time and frequency domains is described. The proposed method employs the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation after applying the mass-lumping procedure is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution. This technique is, therefore, an implicit unconditionally stable finite-element time and frequency-domain scheme, which requires the implementation of the Lanczos process only at the largest time or frequency of interest. Consequently, a multiple time- and frequency-domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time. The efficiency and effectiveness of this new technique are illustrated by using numerical examples of three-dimensional cavity resonators     

采用分部外推BCGS-FFT方法快速求解电磁散射问题

为了快速求解电磁散射问题中具有震荡性、奇异性、慢收敛性的索末菲积分,提出了一种利用分部外推算法加速索末菲尾部积分计算,并结合稳定双共轭快速傅里叶变换(stabilized biconjugate gradient fast Fourier transform,BCGS-FFT)算法求解电磁散射问题场分布情况的新方法. 首先给出电场积分方程(electric field integral equation, EFIE)的表达形式,且在求解过程的索末菲积分中应用一种便捷的椭圆积分路径来最小化索末菲积分的震荡性与奇异性,在索末菲尾部积分使用Levin分部外推法来提高积分收敛速度,以此来快速填充并矢格林函数矩阵. 然后对新方法进行了多种数值实验,验证算法的精确度,并对比了新方法与传统BCGS-FFT方法的计算效率,发现在保持相同计算精度的条件下,新方法可节省20%～37%的计算时间. 该方法能应用于复杂散射体嵌入多层空间的电磁散射计算,为快速求解目标区域的电磁散射场提供了一种新的方法.     

Calculation of the surface-wave excitation in multilayeredstructures

A novel rigorous analysis of the surface waves excited by a Hertzian dipole embedded in a multilayered structure is presented. A transmission-line resonator equivalent circuit is used to calculate the surface wave's electromagnetic field components. It is shown that the power carried by the surface waves is related to the energy stored in the resonator. An analytical method for the calculation of the stored energy is given. A simple algorithm iterating over the layers of the structure is derived to analytically calculate the surface wave's electromagnetic field components and the power carried by surface waves. The need of numerical integration or calculation of residues is omitted. This benefits a reduction in computation time and an improvement in accuracy and versatility of computer-aided design (CAD) programs. The presented method has been implemented in a microwave CAD program. Numerical results for planar antennas are presented     

基于电磁计算理论的雷达成像仿真研究

逆合成孔径雷达在战场监测、导弹突防等方面有着广泛的应用。文中采用电磁计算理论研究雷达成像仿真技术。首先,采用物理光学法得到目标表面电流,计算目标大带宽、多角度范围内散射特性。针对计算量大、耗时长的缺陷,文中采用最佳一致逼近理论拟合出目标在大频带、多角度范围内的散射特性,通过计算验证,在不影响精度的前提下大大提高了计算效率;接着,利用计算得到的散射数据,构建宽带目标回波信号,利用转台理论,进行小角度内的距离-多普勒成像;最后,以锥台为例,计算了从不同角度入射时的目标雷达图像,可以验证该方法的正确性和高效性。     

Cellular handsets antenna modeling by vector finite element method

An algorithm of electromagnetic fields simulation and calculation of cellular handsets antenna parameters by vector finite element method in frequency domain is presented. The algorithm is based on discretization of the electric field equation by Galerkin method using basis functions of various order. Incorporation of lumped elements and ports into finite element model is provided. Fast frequency sweep is used for accelerating solution process in a wide frequency band. Comparison of simulation and experimental results proves high accuracy and reliability of the developed computer code.     

Passive equivalent circuit of FDTD: an application to subgridding

The finite difference time domain (FDTD) method gives accurate results for many problems but uses a large amount of computer memory and time. This can be reduced by using subgrids (fine grids) only around critical areas in the problem domain. The fields within the coarse and fine grids are found using standard FDTD equations, while at the boundary of the subgrid, interpolation of coarse grid fields is utilised. However, a simple interpolation as reported in literature exhibits late time instability. The authors present a stable scheme of updating the subgrid boundary fields by replacing the grid discontinuity with an equivalent circuit. The stability and accuracy of this new scheme is demonstrated through calculation of the cutoff wavelength of a dielectric slab loaded waveguide for various slab thickness     

基于LOD-FDTD的微带线边缘奇异性处理技术研究

为解决现有方法在处理微带线边缘电磁场的奇异性时,存在计算效率和精度之间的矛盾,该文提出一种在局部1维时域有限差分法(LOD-FDTD)基础上,结合微带线边缘电磁场分布函数,并通过坐标变换可处理导体嵌入网格面积大于1/2时的情况,因而适用性更广的微带线边缘奇异性处理技术。与现有奇异性处理技术对比证明,该算法在采用的时间步长小于等于Courant-Friedrichs-Lewy(CFL)稳定性条件所允许最大时间步长5倍的情况下,具有更高的计算精度。且与一般LOD-FDTD算法对比证明,引入的微带线边缘电磁场分布函数使得该算法在节省计算资源和提高计算效率的同时,保持了更高的计算精度。     

外场作用双导线的电磁耦合时域分析方法

基于时域有限差分（finite-difference time-domain，FDTD）法和传输线方程，并结合插值技术，研究了一种高效的时域混合算法，能够快速模拟电磁波照射自由空间和屏蔽腔内双导体传输线的电磁耦合，并实现空间电磁场与双导线瞬态响应的同步计算.该算法先采用FDTD方法模拟双导线周围空间的电磁场分布，结合插值技术构建适用于双导线电磁耦合的传输线方程，再采用FDTD的中心差分格式进行离散，从而求解得到传输线和端接负载上的瞬态响应.同时，分析双导线间距对其电磁耦合的影响，掌握其耦合规律.通过相应数值算例的模拟，并与FDTD方法进行对比，验证了该时域混合算法的正确性和高效性.     

Three-dimensional analysis of electromagnetic fields in rectangularwaveguides by the boundary integral equation method

A rapidly convergent expression of electromagnetic fields in rectangular waveguides is proposed for three-dimensional electromagnetic field analysis by using the integral equation method. The new method is an improved image expansion method utilizing the rapid convergence of the orthogonal expansion method. By this new method, the slow convergence of the orthogonal method with currents near an observation point can be removed completely. In order to investigate the adequacy of the new expression, the fields produced by the line electric and magnetic current segments are calculated and compared with the values obtained by the orthogonal expansion method. This confirms that the new expression gives accurate numerical values with a short computing time. Electromagnetic fields in a rectangular waveguide with circular metallic and dielectric posts are analyzed by using the new expression. From computed values, equivalent circuits of the metallic and dielectric post are obtained and compared with values obtained by N. Marcuvitz (1951). Reasonably good agreement is obtained     

混合ACA和MLFMA方法计算复合目标电磁散射

采用矩量法(MoM)计算电大尺寸的复合目标的电磁散射。为了能够高效快速地计算电大尺寸三维复合目标的电磁散射,提出一种新的混合方法,将自适应交叉近似(ACA)算法和多层快速多级子(MLFMA)算法相结合,共同加速矩量法的计算。其中,MLFMA用于加速目标与自身的作用,ACA用于加速目标与其他目标的相互作用。提出的混合算法在计算复合目标电磁散射时,可降低运算存储,缩短阻抗矩阵填充时间,并且能够加快矩阵矢量乘,且不影响计算精确度。数值算例表明,所提快速算法能够在保证电磁散射计算精确度前提下,比传统方法更高效。     

电磁计算中辛时域有限差分算法研究进展

辛时域有限差分（symplectic finite-difference time-domain，SFDTD）算法作为一种高精度、高稳定、高保真度的时域数值算法，在多个学科领域得到了广泛的应用，并已发展成为一种较为成熟的数值计算方法.本文主要对SFDTD算法的构建、数值优化以及相关关键技术处理进行了介绍.重点总结了基于时间和空间上的差分近似优化处理方法，处理不连续边界及金属曲面时的局部修正方法，以及时域电磁仿真中不可或缺的三大关键技术:总场/散射场技术、完全匹配层（perfect matched layer，PML）、近远场变换技术.最后，介绍了SFDTD算法在电磁仿真、量子力学求解、多物理问题建模与分析中的具体应用.     

A higher order FDTD method in Integral formulation

We present a fourth-order (4, 4) finite-difference time-domain (FDTD)-like algorithm based on the integral form of Maxwell's equations. The algorithm, which is called the integro-difference time-domain (IDTD) method, achieves its fourth-order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell. In the algorithm, the electromagnetic fields within each cell are represented by space and time integrals (or integral averages) of the fields, i.e., the electric and magnetic fluxes (D,B) are represented by the surface-integral average, and the electric and magnetic fields (E,H) by the line and time integral average. In order to relate the integral average fields in the staggered update equations, we have obtained constitutive relations for these fields. It is shown that the IDTD update equations combined with the constitutive relations are fourth-order accurate both in space and time. The fourth-order correction terms are represented by the modified coefficients in the update equations; the numerical structure remains the same as the conventional second-order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth-order accuracy in time. Furthermore, the Courant-Friedrichs-Lewy (CFL) stability criteria of this fourth-order algorithm turns out to be identical to the stability limits of conventional second-order FDTD scheme based on differential formulation.     

并矢分析在电磁场求解中的应用

给出广义电磁场矢量和并矢波动方程的格林函数积分解,在物理定律和边界条件的约束下,用并矢分析的方法证明了两解的同解性,并对自由空间并矢格林函数的对称性进行了并矢分析展开验证。结合并矢分析法求解电磁场的两个应用实例,表明并矢分析法相对于传统方法具有简捷明了的特性。     

利用近场Gordon积分近似的矩量法-物理光学混合方法

针对电大金属目标的电磁计算, 提出了一种新的矩量法-物理光学(Method of Moment-Physical Optics, MoM-PO)混合方法, 以解决传统的MoM-PO混合法中PO区域和MoM区域耦合项的计算时间过长问题.用Gordon积分计算目标的PO区域对MoM区域的作用, 并加入近场近似处理.该方法避免了传统的MoM-PO混合法中耦合项积分方程的计算, 加大PO区域的剖分面元的大小, 能够有效地降低矩阵规模和未知数个数, 因而降低了内存, 减少了计算时间.数值算例结果表明, 近场Gordon积分近似的MoM-PO混合方法能够有效地减少耦合项的计算时间, 并能达到理想的精度.     

基于MATLAB对二维混合边界静电场域的分析

本文分析了有限差分法的原理与概念,讨论了电磁场问题涉及3种类型的边界条件,采用有限差分数值计算分析边界问题,对二维混合型边界静电场进行分析,用MATLAB编程计算差分方程,并将超松弛迭代法引入到差分方程的计算,并与简单迭代方法进行比较,同样的计算精度下采用超松弛法不仅节省存储空间,而且加快了收敛速度。通过计算可以看出MATLAB在解决实际的工程和数学问题中,具有使用更为简便、语句功能更强的特点,能直观地演示二维混合边界静电场的电势分布图和场强立体分布图。     

La méthode RTL Un concept hybride pour l’analyse du rayonnement des cartes électroniques

This study deals with an hybrid method to analyse the radiation of printed circuit board. This method (the rtl) is hybrid because it mixes both the transmission lines concept and the principle of reciprocity. The transmission lines concept gives currents on the radiating devices and the principle of reciprocity allows to calculate the electromagnetic field. This hybrid concept offers many benefits like rapidity and accuracy. It allows studies of difficult devices with a short time of calculation. The results from the rtl method are checked with experimental measurements and by comparison to commercial softwares.     

Electromagnetic and thermal analysis for lipid bilayer membranesexposed to RF fields

Experiments with pulsed radio frequency fields have shown influence on the low-frequency behavior of lipid bilayer membranes. In this paper, we present an electromagnetic and thermal analysis of the used exposure device to clarify whether the observed effects have a thermal cause and to determine the fields at the lipid bilayer. In order to model the very thin lipid bilayer (about 5 nm) accurately, the electromagnetic analysis is broken into several steps employing the finite difference time domain technique and a finite element/boundary element hybrid approach. Based on the obtained power loss due to the electromagnetic fields, the temperature change is calculated using the finite element method for the solution of the heat conduction equation. Both, the electromagnetic and the thermal analysis are performed for a variety of material parameters of the exposure device. The electromagnetic analysis shows that the exposure device is capable of producing voltages on the order of 1 mV across the lipid bilayer. The combined electromagnetic and thermal calculations reveal that the temperature oscillations due to the pulsed radio frequency fields are too small to directly influence the low-frequency behavior of the lipid bilayer.