等离子体的交替方向隐式时域有限差分方法

首次把交替方向隐式时域有限差分法(ADI-FDTD)推广到色散介质——无碰撞非磁化等离子体中,计算了非磁化等离子体与电磁波的相互怍用,使用ADI技术给出了无碰撞等离子体介质中的ADI-FDTD迭代公式．并解析地证明了等离子ADI-FDTD算法也是无条件稳定的,数值计算表明,等离子体ADI-FDTD算法与传统的FDTD的计算结果吻合,计算效率更高。     

Dispersion compensation for Huygens' sources and far-zonetransformation in FDTD

The equivalence principle is utilized for generation of both incident plane waves and for near- to far-zone transformation in the finite-difference time-domain (FDTD) method. Small errors will appear due to numerical dispersion when a plane wave is generated by Huygens' sources using an analytical expression for the incident field. These errors can be derived from the numerical dispersion relation in the frequency domain. By using a second-order approximation of the numerical wavenumber it is shown that a simple approximative time-domain compensation procedure for the dispersion can be derived. This has been implemented in a Huygens' source routine and in a time-domain near- to far-zone transformation routine. It is shown that this compensation significantly reduces the errors produced when calculating far-zone scattered fields of low amplitude. It is also shown that it is sufficient to compensate either the Huygens' sources or the time-domain near- to far-zone transformation with respect to dispersion. For validation, plane wave propagation through empty space and scattering of a dipole have been studied     

Time-domain modeling of electromagnetic wave interaction with thin-wires using TLM

A method for the time-domain simulation of electromagnetic (EM) wave interaction with thin-wires is developed. The technique is based on the standard transmission-line modeling (TLM) technique augmented with systems derived from the telegrapher's equations to represent the propagation of currents in wires. Full details of the numerical algorithms are given and examples are shown to illustrate the application of the technique to typical electromagnetic compatibility (EMC) problems.     

Formulation of probe-corrected planar near-field scanning in thetime domain

Probe-corrected planar near-field formulas in the time domain are derived for both acoustic and electromagnetic fields, so that a single set of near-field measurements in the time domain yields the fields of the test antenna directly in the time domain. The time-domain probe-corrected formulas are first derived by taking the inverse Fourier transform-of the corresponding frequency-domain formulas, and then by using a time-domain expansion for the fields of the test antenna and a time-domain receiving characteristic of the probe. Because these general formulas, which involve a double integral over the scan plane and an infinite time-convolution integral, are rather complicated, we consider a special probe whose output due to an incoming time domain plane wave is proportional to the time derivative of the field of that plane wave. For this special “D-dot probe”, the probe-corrected formulas simplify to give the time-domain far-held pattern as a double spatial integral of the time-domain output of the probe over the scan plane multiplied by the angular dependence of the inverse receiving characteristic of the probe. Time-domain reciprocity relations are derived for reciprocal probes, and their time-domain receiving characteristics are related to their far fields. Finally, a time-domain sampling theorem is derived and a numerical example illustrates the use of the time-domain probe-corrected formulas     

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.     

A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion

A highly accurate and numerically stable model of Lorentz dielectric dispersion for the finite-difference time-domain (FDTD) method is presented. The coefficients of the proposed model are optimally derived based on the Maclaurin series expansion (MSE) method and it is shown that the model is much better than the other four reported models in implementing the Lorentz dielectric dispersion with error of relative permittivity several orders lower. The model's stability and performance are also analyzed when it is incorporated into the practical second- and fourth-order accurate FDTD algorithms for an exemplified Lorentz medium. Interestingly, we find that all the mentioned models show nearly the same performance in the second-order algorithm due to its large intrinsic numerical dispersion and the superiority of the proposed MSE model begins to be manifested in the higher-order, say, fourth-order FDTD algorithms as implied by the governing numerical dispersion equations.      

PML吸收边界的时域有限差分法的数值色散研究

PML吸收边界以其优异的吸收能力与效果而倍受人们的关注。本文针对运用PML吸收边界的时域有限差分法的数值色散问题进行了研究,并得到了较为满意的结果,PML吸收边界在有效减少电磁 波在边界上的反射的情况下,并没有带来对数值色 散的不良影响。     

A method for calculation of the characteristics of a system of parallel dipoles excited by stationary and pulse signals

Problems of diffraction of a monochromatic wave and an electromagnetic pulse by a system of parallel dipoles are considered. For these problems, integral equations (IEs) for the density of the current distribution are derived and solved. A method for solution of the IEs is proposed that involves separating the static component of the IE kernel, making allowance for the singularity of the current distribution on the dipoles’ ends, and subsequently applying of the collocation method. The far-zone field is calculated for the problems of pulse excitation and diffraction. The time of the frequency-domain computation is compared to the time of the time-domain computation followed by recalculation to the frequency domain.     

Time-Domain Analysis of Millimeter Wave Circulation Around a Magnetised Ferrite Sphere

An efficient numerical method has been devised for the study of wave circulated by a magnetised ferrite sphere. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. The electromagnetic fields inside the ferrite body are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained in a wide frequency band with a single time domain run. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide / microstrip junction circulators.     

Finite-difference approach to the solution of time-domain integralequations for layered structures

A numerical algorithm for the analysis of transient electromagnetic fields in planar structures is proposed based on the time-domain magnetic-field integral equation (MFIE), electric-field integral equation (EFIE), and the marching-on-in-time approach. The field vectors are represented in terms of vector potential functions which are calculated either by integration or by the three-dimensional (3-D) wave equation according to the geometry of the structure. Thus, the algorithm combines the advantages of integral equation techniques and finite-difference schemes. While this approach is applicable to any geometries, it is especially suitable for multilayered planar structures and is competitive to the finite-difference time-domain (FDTD) method in the case of open and radiating problems. Theoretical results are verified by the analysis of a pulse propagation in a homogeneous open-end microstrip line     

Numerical solution of time domain integral equations for arbitrarily shaped conductor/dielectric composite bodies

In this work, we present a numerical solution of the coupled time domain integral equations to obtain induced currents and scattered far fields on a three-dimensional, arbitrary shaped conducting/dielectric composite body illuminated by a Gaussian electromagnetic plane wave pulse. The coupled integral equations are derived utilizing the equivalence principle. The solution method is based on the method of moments and involves the triangular patch modeling of the composite body, in conjunction with the patch basis functions. Detailed mathematical steps along with several numerical results are presented to illustrate the efficacy of this approach.     

烟幕扩散模型中任意光路电磁波透过率的计算

在烟幕扩散模型中,计算电磁波沿任意路径穿透烟幕云团时产生的衰减,需要准确计算出该路径下的烟幕积分浓度,从而得到电磁波的透过率。本文基于空间几何坐标变换原理、线性代数矩阵运算方法以及烟幕材料消光理论,推导了烟幕扩散模型中电磁波入射方向改变时的三维坐标系变换矩阵和二维积分浓度投影算法,实现了电磁波沿任意方向入射时的积分浓度分布及透过率的计算,为烟幕扩散模型的多角度(方向)数据分析、烟幕云团红外图像处理以及更多应用场景中的使用奠定了基础。     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

An efficient formulation to determine the scatteringcharacteristics of a conducting body with thin magnetic coatings

Two new and efficient surface integral equations, derived from corresponding volume integral equations, are developed to calculate the scattering of electromagnetic (EM) waveform from an arbitrarily shaped conducting body coated with thin lossy magnetic film. Their numerical solutions by the method of moments (MM) for two-dimensional structures with full or partial coatings are presented. It is shown that the radar cross-section of a conducting body can be significantly reduced by coating it with a lossy magnetic film. To verify the validity and accuracy of the proposed formulation, another method based on the expansion of cylindrical harmonic functions with real arguments is also developed to calculate the scattering of a plane EM wave from an electrically large coated circular cylinder. The same problem was also solved by the proposed formulation, and excellent agreement between the two approaches was achieved. In addition, numerical results of the scattering from a rectangular coated cylinder is shown to be consistent with that obtained by a modified finite-difference-time-domain (FDTD) method     

Survey on Symplectic Finite-Difference Time-Domain Schemes for Maxwell's Equations

To discretize Maxwell's equations, a variety of high-order symplectic finite-difference time-domain schemes, which use th-order symplectic integration time stepping and th-order staggered space differencing, are surveyed. First, the order conditions for the symplectic integrators are derived. Second, the comparisons of numerical stability, dispersion, and energy-conservation are provided between the high-order symplectic schemes and other high-order time approaches. Finally, these symplectic schemes are studied by using different space and time strategies. According to our survey, high-order time schemes for matching high-order space schemes are required for optimum electromagnetic simulation. Numerical experiments have been conducted on radiation of electric dipole and wideband S-parameter extraction of dielectric-filled waveguide. The results demonstrate that the high-order symplectic scheme can obtain satisfying numerical solutions under high Courant-Friedrichs-Levy number and coarse grid conditions.     

Extended integral equation formulation for scattering problems froma cylindrical scatterer

An extended integral equation is developed for electromagnetic scattering from a perfectly conducting cylinder and a dielectric cylinder. The conventional surface integral equations cannot yield unique solutions when the wavenumber of the electromagnetic wave is equal to an eigenwavenumber of the system. Several methods to overcome this difficulty have been presented, but each method includes some drawbacks. A numerical method is proposed in which the boundary element method is applied to the extended integral equations with the observation points lying on a closed surface inside the scatterer. It is shown that the extended integral equations have unique solutions for any given wavenumber. As examples, plane wave scattering from a perfectly conducting elliptic cylinder, a dielectric elliptic cylinder, and a dielectric rectangular cylinder is numerically analyzed     

Edge diffraction in the vicinity of the tip of a composite wedge

The electromagnetic field due to a line source radiating in the presence of a two-dimensional composite wedge composed of a number of conducting and dielectric materials is obtained. The Fourier transform path integral method (FTPI) is described and used to perform the numerical analysis. An important feature of the FTPI method is that it is based on a global solution to the Helmholtz scalar wave equation. As such the method avoids numerical enforcement of boundary conditions and the necessity of reformulating the analytical/numerical equations for each geometric configuration. The total scattered field is presented for several cases where one of the dielectric wedge sections is lossy, including examples of microwave scattering from a crested ocean surface and an air-ocean-sea ice interface     

Numerical dispersion and stability characteristics of time-domainmethods on nonorthogonal meshes

The familiar finite-difference time-domain method for discretizing Maxwell's curl equations on orthogonal grids has been extended to nonorthogonal grids by a number of researchers. While it is difficult to determine the dispersion and stability characteristics of these methods when applied on arbitrary grids, analysis of the idealized but representative case of a uniform skewed mesh proves to be quite tractable in 2-D. This analysis demonstrates that numerical dispersion errors are small for well-resolved spatial wavelengths and that these methods converge to the continuous-space solution in the limit as the cell and time step sizes vanish. Grid anisotropy (variations in wave propagation speed as a function of the propagation angle relative to the mesh coordinates) increases as the mesh is skewed. In spite of this, there exist some angles where waves propagate through the skewed mesh with virtually no dispersion. This analysis also provides a stability limit for the time step size in terms of geometrical mesh quantities     

FDTD Study on Back Scattering of Conducting Sphere Coated with Double-Negatibe Metamaterials

The shift operator method in finite-difference time-domain method for anisotropic double-negative (DNG) metamaterials is derived. The problem which incorporates both anisotropy and frequency dispersion at the same time is solved for the electromagnetic wave propagation in DNG media. By comparing with the mie series solution, the numerical verification of the method and program are confirmed by computing the back scattering of isotropic unmagnetized plasma sphere. The back scattering of conducting sphere coated with DNG media with different parameters is computed by using the shift operator method. One finds that the degree of DNG media’s match and isotropy plays important parts in the decrease of the back scattering of the conducting sphere.