细线结构时域电场积分方程的有限差分求解

提出一种求解基于细线结构的时域电场积分方程 ( TDEFIE)的方法 -有限差分方法。与传统求解时域电场积分方程的时域矩量法相比 ,该方法易于数值实现。文中还利用该方法研究了电磁辐射、散射的三个经典问题 ,并将结果与时域矩量法的结果进行了比对 ,研究表明 ,该方法求解细线结构的 TDEFIE非常有效。     

Stabilisation procedure for electric field integral equation

A stabilisation procedure for the electric field integral equation (EFIE) is developed which renders the EFIE stable with respect to the discretisation interval used to numerically solve the equation. Representative numerical examples are provided which demonstrate the effectiveness of the procedure     

Singular basis functions and curvilinear triangles in the solutionof the electric field integral equation

Basis functions are formulated that account for singularities in the charge density near an edge on a conducting body. The formulation is general and the basis functions are valid for planar as well curvilinear geometries. In principle, singularities of any order can be treated, but best results are obtained for so-called “knife edge” singularities. Results are compared with exact solutions or measurements where available for some simple problems     

Solution of time domain electric field Integral equation using the Laguerre polynomials

In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.     

On the domain integral equation method for anisotropicinhomogeneous waveguides

The domain integral equation method for anisotropic inhomogeneous dielectric waveguides is derived, and the spectral properties of the integral operator are discussed. It is explained why spurious modes do not occur when the Galerkin method is applied to the domain integral equation. Furthermore, the convergence of the method is discussed     

A new temporal basis function for the time-domain integral equationmethod

A new temporal basis function that has all-order continuous derivative has been constructed using a nonlinear optimization scheme. This new basis function provides a much more stable explicit marching-on-in-time (MOT) solution, based on the time-domain integral equation (TDIE) method, than that presently available. Two examples are presented to illustrate the superior stability of the proposed temporal basis function     

基于时域体面积分方程的分块预条件方法

时域体电场积分方程性态较好,但时域面积分方程性态较差,这就造成体面耦合的时域电场积分方程在迭代求解时经常遇到收敛较慢的问题,无法满足工程需要,并且一般预条件技术获得的加速效果也不甚理想。因此,时域体面积分方程迭代求解时间过长已成为体面积分方程在实际工程应用中的核心问题。针对时域体面电场积分方程矩阵性态差的问题,提出一种引入分块预条件方法(BMP),可以加快矩阵迭代收敛的速度。将时域体面积分方程的矩阵分解成3块矩阵相乘的形式,而这3块矩阵都是稀疏的,并通过几个体面算例说明该预条件技术的效率。     

Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.     

Combined circuit-electromagnetic simulation using multiregion time domain integral equation scheme

A full-wave time domain integral equation based formulation for broadband modeling of finite conductors and dielectrics in high-speed microelectronics is presented. An efficient and accurate coupling scheme is developed to enable surface integral equations to couple to modified nodal analysis for combined circuit-electromagnetic systems such as those arising in microwave and RF circuits.     

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.     

Physical and analytical properties of a stabilized electric field integral equation

The physical and analytical properties of a stabilized form of the electric field integral equation are discussed for closed and open perfectly conducting geometries. It is demonstrated that the modified equation provides a well-conditioned formulation for smooth geometries in both the high- and low-frequency limits; an instability remains near the edges of open geometries, requiring future consideration. The surface Helmholtz decomposition is used to illustrate the mechanism of the stabilization procedure, and the relevance of this mechanism to the numerical discretization of the equation is outlined.     

基于积分方程区域分解算法的研究进展

介绍了近年来用于电磁建模的积分方程区域分解算法（domain decomposition method,DDM）.DDM是一种基于"分而治之"策略的框架性算法,为复杂电磁问题的求解提供了一种灵活的技术途径.结合国内外研究动态详细介绍了三类积分方程DDM,即重叠型积分方程DDM,非共形、非重叠型积分方程DDM以及基于等效原理的积分方程DDM,并通过数值算例说明了这些算法的优缺点.最后总结了积分方程DDM的主要挑战以及展望.     

电场积分方程矩量法中具有局部连续性的基函数积分奇异性降阶处理

三维散射与辐射问题常基于电场积分方程(EFIE),运用矩量法求解。该文证明了只要所选择的屋顶基函数(rooftop basis functions)具有局部连续性,无论对于平面或者曲面单元,都能将求解阻抗矩阵元素的积分函数写成一种对称形式,使得其奇异性降为 O(1/R),从而避免了现有文献中因处理源点和观察点重合时出现的O(1/R2)奇异性所导致的积分复杂性,数值计算结果表明了简化后计算公式的有效性和可靠性。     

时域MEI方法初探

对时域ＭＥＩ方法进行了初步探索,根据ＭＥＩ方法的基本原理,建立起时域ＭＥＩ方法的一阶吸收边界条件,应用该条件对线源辐射问题的数值实验和研究表明,它可使截断边界离源更近,同时也证实了时域ＭＥＩ方法的可靠性和精确性。     

A space-time discretization criterion for a stable time-marchingsolution of the electric field integral equation

Numerical techniques based on a time-domain recursive solution of the electric field integral equation (EFIE) may exhibit instability phenomena induced by the joint space-time discretization. The above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape. We analyze a particular formulation of the method of moments which relies on a triangular-patch geometrical model of the exterior surface of the scattering body and operates according to a “marching-on-in-time” scheme, whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps. A heuristic stability condition is devised which allows us to define a proper time step, as well as a geometrical discretization criterion, ensuring convergence of the numerical procedure and, therefore, eliminating insurgence of late-time oscillations. The stability condition is discussed and validated by means of a few working examples     

Transient electromagnetic scattering from dielectric objects using the electric field Integral equation with Laguerre polynomials as temporal basis functions

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared.     

电介质半空间两耦合线天线的时域积分方程法

直接从时域为两平行线天线受电磁脉冲激励的瞬态过程建模,建立了自由空间中、大地视为理想导体和有损媒质时两天线耦合的仅由矢量磁位表达的时域积分方程组,并用时域矩量法(MOM)结合时间步进算法(MOT)快速求解.针对实例的计算结果与文献结果吻合,从中可分析天线间距和离地高度变化时媒质对线上电流的影响规律.在三米法电波暗室的实验进一步验证了算法的有效性.     

Evaluation of LEMP effects on complex wire structures located abovea perfectly conducting ground using electric field integral equation intime domain

In this paper, a novel approach for the implementation of scattering theory is proposed in order to evaluate the electromagnetic effects of lightning return stroke on complex wire structures (lightning EM pulse - LEMP). An electric field integral equation (EFIE) in the time domain is employed to describe the electromagnetic transients from lightning. The proposed approach is applied to a single-phase, three-phase as well as a Y-shaped transmission line located above a perfectly conducting ground. The simulation results reproduce accurately experimental data available in the literature. The proposed method provides new possibilities in estimation of lightning indirect effects on complex networks as an example “radial transmission systems tapped from main switching substations” are investigated     

矩量法精确求解磁场积分方程的有效方法

矩量法求解磁场积分方程（MFIE)迭代收敛快,但计算精度不高. 通过提取和处理MFIE积分核中的强奇异点,并采用积分域变换消除方程中残留弱奇异性的方法,使矩量法求解MFIE能达到良好的精度. 计算了模型的雷达散射截面（RCS）MFIE计算结果与电场积分方程（EFIE）结果吻合良好,误差小于0.5 dB,且收敛性优于EFIE,验证了算法的有效性.