The 3-D multidomain pseudospectral time-domain algorithm for inhomogeneous conductive media

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a strongly well-posed perfectly matched layer (PML) is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in inhomogeneous and conductive media. This approach allows for an accurate treatment of curved geometries by multidomain decomposition and curvilinear coordinate transformation. Numerical experiments show the results agree excellently with analytical solutions and results of other well-known algorithms, and demonstrate a remarkable improvement in accuracy and efficiency over the FDTD method. The 3-D multidomain PSTD algorithm is then applied to calculate radar cross sections (RCS).     

Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method

In order to deal with the stability problem restricted by the finite-difference time-domain (FDTD) and conventional pseudospectral time domain (PSTD), the multidomain PSTD algorithm based on alternating-direction implicit (ADI) technique is proposed in this paper. This algorithm improves the stability and efficiency of conventional PSTD, while it maintains the accuracy and flexibility of conventional PSTD for an accurate treatment of arbitrarily curved objects. A compact matrix form is derived to effectively describe two-dimensional ADI multidomain pseudospectral time domain (ADI-MPSTD) algorithm. Numerical results show an excellent agreement with analytical solutions as well as results obtained by the FDTD algorithm, and fully demonstrate a remarkable improvement in stability and efficiency.     

The 3-D multidomain pseudospectral time-domain method for wideband simulation

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a well-posed PML is developed as an accurate and efficient solver for Maxwell's equations in conductive and inhomogeneous media. The curved object is accurately treated by curvilinear coordinate transformation. Spatial derivatives are obtained by the Chebyshev collocation method to achieve a high-order accuracy. Numerical results show an excellent agreement with solutions obtained by the FDTD method under fine sampling.     

有耗媒质中3D目标体散射特性的TSNU-PSTD模拟

结合PML边界条件的傅立叶时域伪谱(PSTD)算法已广泛用于模拟电磁波传播和目标散射,但传统的PSTD方法在每个坐标方向上需要均匀分布的空间坐标网格点,从而不能够很好地模拟曲面目标和与网格空间尺寸不一致的目标,基于变空间的PSTD方法可以很好地克服这些不足。文中将CFS-PML边界条件在PSTD算法中实现并将它与TSNU-PSTD方法结合模拟了大范围有耗媒质中2D\3D曲面介质体目标的电磁散射,部分结果与FDTD计算结果进行了比较。仿真结果表明,基于变空间的PSTD只需平均每波长分成3个网格就可以达到较好的精度,可高效模拟电大尺寸空间曲面形状目标体的电磁散射。     

应用超时间步方法的多区域伪谱时域算法

为了解决时域有限差分算法(FDTD)和伪谱时域算法(PSTD)稳定性方面的不足,本文提出了一种基于超时间步(STS)的多区域伪谱时域算法(STS-MPSTD).该算法不仅具有传统的多区域伪谱时域算法分析任意曲边形体问题时的精确性和灵活性,而且在维持显式时间积分的简单性和精确性的同时也让它不受稳定性条件的约束.最后文中给出的数值实例结果与解析结果完全吻合,这充分证明了该算法具有高的精度和良好的稳定性.     

加权总场法在PSTD算法中的应用

伪谱时域(PSTD)方法可以处理电大尺寸目标电磁散射问题。本文介绍了一种能够把入射波有效引入PSTD计算区域的新方法——加权总场法。该方法通过引入类似于FDTD中连接边界的连接层，将计算区域划分为总场区、连接区和散射场区。为了总场区和散射场区的连续，在连接区引入窗函数．通过设置8—10层连接区就可以将入射波有效地引入到PSTD总场区。这样使入射波和目标分离，实现了复杂目标的单独建模，从而使PSTD便于模拟复杂目标的电磁散射。文中以高斯脉冲为入射波，通过二维情况下目标散射宽度的数值结果，验证了加权总场法应用于PSTD算法时的有效性和计算精度。     

PSTD算法及其吸收边界分析

在解时域电大尺寸电磁场问题时,由于受到有限差分格式二阶精度的限制,传统FDTD算法的效率很低,对内存的要求高.采用以伪谱方法离散Maxwell微分方程为核心的Pseudospectral time-domain(PSTD)算法计算电大尺寸电磁场时域问题,将大大提高计算效率,降低内存需求.本文重点探讨了在PSTD技术中,电大尺寸问题的高效实现,并和传统FDTD算法进行了比较.此外还分析了其吸收边界－完全匹配层(PML)所发挥的作用,PML的设置以及各参数对场吸收的影响.     

The unconditionally stable pseudospectral time-domain (PSTD) method

This letter presents a new time-domain method for Maxwell's equations, in which the unconditionally stable techniques, the alternating direction implicit (ADI) and the split-step (SS) schemes, are developed for the pseudospectral time-domain (PSTD) algorithm to maintain stability while achieving higher accuracy and efficiency over the FDTD method. The multidomain strategy is employed to allow for a flexible treatment of internal inhomogeneities. Numerical results demonstrate the unconditional stability and the second-order accuracy for both ADI- and SS-PSTD algorithms.     

MPSTD算法子域分界面上的CV-PB匹配条件

针对多域伪谱时域算法(MPSTD)中子域分界面两侧为不同介质的情形,将特征变量法与物理边界条件相结合提出一种新的子域分界面匹配条件:特征变量-物理边界(CV-PB)匹配条件,并推导得到一般3D曲线坐标系中子域分界面上的场值更新关系.最后给出的数值实例将其与传统分界面匹配条件在算法稳定性、计算精度方面做了比较.多种情形下的数值仿真表明,该匹配条件比传统匹配条件的数值稳定性更好、精度更高.     

计算电大尺寸建筑物内电波场强的PSTD方法

本文采用一种新的时域数值方法－伪谱时域（ＰＳＴＤ）法来计算电大尺寸建筑物内电波场强。提出了由初始条件技术和一维ＰＳＴＤ方程对入射平面波脉冲进行模拟,并利用纯散射场法和线性插值把平面波引入求解问题空间,有效地解决了ＰＳＴＤ方法中入射波设置问题。数值结果表明这种新方法用于模拟电大尺寸建筑物内电波场强的精度和有效性。     

Applications of the PSTD for scattering analysis

In this paper, we apply a pseudospectral time domain (PSTD) algorithm for calculation of the radar cross section of three-dimensional scattering objects. For the purpose of exciting an incident wave without leading to unwanted Gibbs' phenomenon, we utilize an initial condition-excitation technique. Meanwhile, we adopt the pure scattered field formulation to surmount a difficulty of introducing the incident field into computational space. In addition to accommodating a PSTD near-to-far-zone field transform for far-field computations in the algorithm, we develop a one-dimensional memory-saving storage technique for efficient truncation of computational boundary.     

Simulations of ground-penetrating radars over lossy andheterogeneous grounds

The versatility of the three-dimensional (3D) finite-difference time-domain (FDTD) method to model arbitrarily inhomogeneous geometries is exploited to simulate realistic ground-penetrating radar (GPR) scenarios for the purpose of assisting the subsequent designs of high-performance GPR hardware and software. The buried targets are modeled by conducting and dielectric prisms and disks. The ground model is implemented as lossy with surface roughness, and containing numerous inhomogeneities of arbitrary permittivities, conductivities, sizes, and locations. The impact of such an inhomogeneous ground model on the GPR signal is demonstrated. A simple detection algorithm is introduced and used to process these GPR signals. In addition to the transmitting and receiving antennas, the GPR unit is modeled with conducting and absorbing shield walls, which are employed to reduce the direct coupling to the receiver. Perfectly matched layer absorbing boundary condition is used for both simulating the physical absorbers inside the FDTD computational domain and terminating the lossy and layered background medium at the borders     

Eigenvalue Analysis of Curved Waveguides Employing an Orthogonal Curvilinear Frequency-Domain Finite-Difference Method

An eigenvalue analysis numerical technique for curved closed waveguiding structures loaded with inhomogeneous and/or anisotropic materials is presented. For this purpose, a frequency-domain finite-difference method is developed for a general orthogonal curvilinear coordinate system. The main strength of the technique is the accurate modeling of curved transverse boundaries, as well as curved geometries along the propagation direction, under certain limitations for the latter. This feature avoids the necessity of a fine mesh, while it retains a high accuracy and it is free of any staircase effects. In general, the proposed method shares the finite-element technique capabilities in modeling complex boundaries, while it preserves the finite-difference convenience in handling inhomogeneous and anisotropic material loadings. The resulting eigenvalue-based problem is solved using the Arnoldi algorithm, which exploits the system matrix sparcity and the overall technique is robust, unconditionally stable with minimal computational and memory requirements. Numerical results are validated against analytical results and results from 3-D commercial electromagnetic simulators. Finally, novel results are also given.      

A Hybrid PSTD/ADI-CFDTD Method for Mixed-Scale Electromagnetic Problems

We propose a hybrid technique combining the pseudospectral time-domain (PSTD) method with the alternating-direction implicit conformal finite-difference time-domain (ADI-CFDTD) method to solve 3-D mixed-scale problems in computational electromagnetics. A mixed-scale problem contains both electrically large and relatively homogeneous regions and electrically small fine details, thus poses a significant computational challenge to any single computational method if it is utilized alone. In particular, the ADI-CFDTD method is an unconditionally stable time-domain method with second-order spatial accuracy, and allows the time step to be increased beyond the Courant-Friedrichs-Levy limit; it is suitable for electrically small problem (structure details much smaller than a wavelength) but is inefficient and suffers from large numerical errors for electrically large-scale regions. The PSTD method, on the other hand, is accurate and efficient for regions with large, relatively homogeneous materials, but loses its efficiency for electrically small structures. The hybrid PSTD/ADI-CFDTD method overcomes these disadvantages and is potentially more useful than the individual solvers. The implementation details and numerical accuracy of this hybrid method are examined. Numerical examples demonstrate the advantages of the hybrid PSTD/ADI-CFDTD method     

Time-Domain Analysis of a Lossy Nonuniform Transmission Line

An analytical solution of the coupled Telegrapher's equations for the voltage and current on a homogeneous lossy transmission line is presented. The resulting expression is obtained in the form of an exact time-domain propagator operating on the line voltage and current. It is shown that an application of Simpson's rule yields a simple accurate numerical representation of the propagator that can be used to analyze both homogeneous and inhomogeneous transmission lines. Numerical dispersion in lossy media is examined proving that this method has no numerical dispersion.      

吸波结构前缘翼面散射的快速分析

翼面是飞行器对正向入射波的后向RCS的重要来源，为了减缩翼面的后向RCS，一般可在翼面的前缘改用吸波结构以减小翼面对后向的散射。在建立吸波结构前缘翼面的物理模型后，采用快速多极子方法和矩量法的混合方法，计算不同的金属介质分界面条件下的后向雷达散射截面，经过比较和分析，得出降低飞行器翼面后向雷达散射截面的较优方案。     

Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution

This investigation is concerned with the numerical solution of time-harmonic electromagnetic scattering by axisymmetric penetrable bodies having arbitrary cross-sectional profiles and even continuously inhomogeneous consistency. The initiation of this effort involved the discovery and development of the coupled azimuthal potential (CAP) formulation, which is valid in generally lossy isotropic inhomogeneous rotationally symmetric media. Electromagnetic fields in such regions can be represented, using the CAP formulation, in terms of two continuous potentials which satisfy a self-adjoint system of partial differential equations or, equivalently, a variational criterion. Using an optimized variational finite-element algorithm in conjunction with a triregional unimoment method, a versatile computer program is described that provides scattering solutions for each of multiple incident fields impinging upon an arbitrarily shaped inhomogeneous penetrable body of revolution. An extensive evaluation of the accuracy and convergence of the algorithm is presented, which includes comparison of scattering computations and experimental measurements atX-band for several solid and hollow plexiglas bodies of revolution with maximum interior dimensions of over 4 wavelengths.     

Image reconstruction from real scattering data using an iterativescheme with incorporated a priori information

The two-dimensional inverse electromagnetic-scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed from measured far-field scattering data, provided by the USAF Rome Laboratory Electromagnetic Measurement Facility in Ipswich. The targets in the Ipswich data set include perfectly electrically conducting (PEC) targets, penetrable (PEN) targets, and hybrid targets. A new method, which incorporates a priori information about the material properties, is proposed to solve the nonlinear inverse-scattering problem     

An FDTD algorithm with perfectly matched layers for generaldispersive media

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media     

Diffraction tomographic algorithm for the detection ofthree-dimensional objects buried in a lossy half-space

A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm