Z-transform-based FDTD algorithm for anisotropic perfectly matched layer

An efficient method based on the Z-transform theory and the D-H anisotropic perfectly matched layer formulations is presented for truncating general FDTD grids. The formulations are simple and independent of the material properties of the FDTD domain. Numerical examples for radiation and guided-wave problems are included to validate the proposed formulations.     

State-space FDTD implementation of anisotropic perfectly matched layer

New formulations based on the state-space approach are presented for implementing the anisotropic perfectly matched layer into the finite difference time domain (FDTD) algorithm. The formulations are simple and independent from the material properties of the FDTD computational domain. Numerical tests are included to validate the proposed formulations.     

Digital filtering technique for the FDTD implementation of the anisotropic perfectly matched layer

A new algorithm is presented for the finite difference time domain (FDTD) implementation of the anisotropic perfectly matched layer (PML) using the digital signal processing. The algorithm is based on modeling the anisotropic PML region as a set of infinite-impulse response (IIR) digital filters. The advantage of the proposed method is that it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are implemented using D and B fields rather than E and H, and this allows the PML to be independent from the material properties of the FDTD computational domains. Numerical tests have been carried out in two dimensions to validate the formulations.     

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     

DSP techniques for implementation of perfectly matched layer fortruncating FDTD domains

A new algorithm for implementing the perfectly matched layer (PML) using digital signal processing (DSP) is presented for truncating finite difference time-domain (FDTD) domains. The algorithm is based on incorporating digital filtering techniques into the PML formulation. A simple, unsplit-field and material independent PML formulation is achieved     

Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.     

A new anisotropic perfectly matched layer medium for mesh truncation in finite difference time domain analysis

In this paper an unsplit anisotropic perfectly matched layer (PML) medium, previously utilized in the context of finite element analysis, is implemented in the finite difference time domain (FDTD) algorithm. The FDTD anisotropic PML is easy to implement in the existing FDTD codes, and is well suited for truncating inhomogeneous and layered media without special treatment required in the conventional PML approach. A further advantage of the present approach is improved performance at lower frequencies. The applications of the unsplit anisotropic PML/FDTD method are illustrated by considering the problems of a plane wave propagation and an open microstrip line.     

Perfectly matched layer-absorbing boundary condition for left-handed materials

The perfectly matched layer (PML) absorbing boundary condition (ABC) is extended to truncate the boundary of left-handed materials in the Finite-Difference Time-Domain (FDTD) simulation. The uniaxial material parameters are given in the frequency domain, and discretized in the FDTD update procedure by means of the Z-Transform technique. The effectiveness of the PML is demonstrated by numerical results.     

A digital filter approach for complex frequency-shifted perfectly matched layer in semivectorial FDTD

A new formulation of the perfectly matched layer (PML) for the semivectorial finite-difference time-domain (FDTD) method in optical waveguide simulation is presented by incorporating the infinite-impulse response (IIR) digital filter technique. The complex frequency-shifted PML is implemented through Z transformation, where the second-order derivatives in semivectorial FDTD are realized by two cascaded first-order recursive IIR digital filters. The numerical examples indicate that the new scheme has better performance compared with the normal PML.     

Extension and validation of a perfectly matched layer formulation for the unconditionally stable D-H FDTD method

In this letter, a modification to the recently proposed unconditionally stable D-H ADI FDTD method is presented that considerably reduces the late-time error induced by the corner cells. The PML boundary is derived from the direct discretization of the modified D-H Maxwell's equations rather than the superposition of uniaxial PML boundaries. An optimal choice of the PML conductivity profile coefficients is proposed. Results show that the reflection error of the PML is limited for increased time step size beyond the Courant-Friedrichs-Lewy stability bound, and maximum reflection errors are 15 to 20 dB lower than the original formulation.     

UPML媒质中无条件稳定的二维ADI-FDTD方法

对单轴各向异性PML（UPML）媒质中二维TM波的交变方向隐式时域有限差分方向（ADI-FDTD），通过计算实例表明，ADI-FDTD方法在UMPL媒质中是无条件稳定的，其时间步长不受CFL稳定性条件的限制，并且当计算区域内具有精细差分网格时，其计算效率明显优于传统的时域有限差分方向（FDTD）。     

三维新型非分裂场完全匹配层吸收边界条件

研究了一种3D新型时域有限差分法（FDTD）非分裂场近似完全匹配层（NPML）吸收边界。在直角坐标系中,通过直接对麦克斯韦方程组中的空间偏导的变量进行空间坐标拉伸,得到三维非分裂场的NPML吸收边界,这种吸收边界相对于PML吸收边界编程实现简单,编程复杂度低。通过对三维算例的电磁散射分析,验证了NPML吸收边界的正确性。计算结果表明了该方法是一个完美的吸收边界,可以用于实际目标的电磁散射问题分析。     

广义柱形坐标系各向异性完善匹配吸收媒质

Ｂｅｒｅｎｇｅｒ提出的完善匹配层只能用于直角坐标系。本文将完善匹配各向异性吸收媒质推广到广义柱形坐标系。推导是在广义柱形坐标系均匀媒质的Ｍａｘｗｅｌｌ方程与直角坐标系各向异性媒质的Ｍａｘｗｅｌｌ方程之间等效基础上进行的。得出了广义柱形坐标系完善匹配层电导率计算公式。     

电各向异性介质FDTD并行算法的研究

基于消息传递模式的网络并行计算系统和区域分割技术成功地实现了电各向异性介质FDTD并行算法,并用此程序代码计算了电大目标的RCS.经测试,该程序代码并行效率达到87%.根据电各向异性介质FDTD迭代式,电场某一节点的计算,需牵涉到其周围28个节点的电磁场值,详细分析了该情况下并行算法中的数据通讯规律,并实现了局域网内各节点机的协同并行计算.数值结果表明了该算法和程序的正确性及优越性.     

电各向异性介质FDTD并行算法的研究

基于一种改进的Z变换-时域有限差分(Z-Finite-Difference Time-Domain, Z-FDTD)方法, 即将双各向异性色散介质的频域本构方程先转化到Z域中, 再利用Z变换的性质将其转换到时域, 得到离散时域的FDTD迭代式, 分析了双各向异性色散介质电磁波传播特性.由于Omega媒质是一种典型的双各向异性色散介质, 以此为例编程计算了垂直入射在Omega介质板情形下产生的同极化和交叉极化电磁波的反射和透射情况, 并通过算例和解析解对比验证了算法的正确性, 最后对其电磁散射特性进行了分析.

     

A mode-preserving perfectly matched layer for optical waveguides

For numerical simulation of wave propagation in optical waveguides, we develop a mode-preserving boundary condition for the popular perfectly matched layer, which truncates the unbounded transverse plane. The method is particularly useful for single-mode longitudinally varying wave-guiding structures and it is easy to use for step-index planar waveguides. With this boundary condition, accurate numerical solutions can be obtained in a much smaller computational window. Numerical results based on the beam propagation method for a tapered waveguide are used to demonstrate the capacity of this boundary condition.     

Application of an anisotropic perfectly matched layer absorber for open boundary truncation in the multiresolution time domain scheme

We apply an anisotropic perfectly matched layer (APML) absorber for open boundary truncation in implementation of the multiresolution time domain (MRTD) scheme. We develop an APML update algorithm to handle a general APML region in the MRTD formulations with the content of the leapfrog algorithm applied in the conventional finite-difference time-domain method. We also discuss the boundary truncations for both perfectly electric conductor (PEC) and perfectly magnetic conductor (PMC) walls using the image techniques. We validate the algorithm by analyzing various guided wave and antenna structures. It is found that the APML performs well for absorbing electromagnetic waves in the MRTD algorithm.     

FDTD法分析涂覆各向异性材料金属目标宽带散射特性

采用时城有限差分方法研究了涂覆各向异性材料金属目标的宽带散射特性,得到了涂覆不同厚度的正单轴和负单轴各向异性材料情况下的频率响应和双站RCS,通过对这些散射数据的分析得出了一些关于涂覆材料及涂覆厚度对目标散射特性影响的结论,这些结论有助于对各向异性隐身材料的研究,体现了时域计算对于分析目标宽频带散射特性的优点.     

理想匹配层的综合优化

本文讨论了理想匹配层的吸收性能 ,给出了一种有效截断理想匹配层的边界条件 ,分析了不同导率剖面和边界条件对理想匹配层吸收性能的影响 ,给出了最小反射意义下的优化理想匹配层。     

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

An efficient multilevel fast multipole algorithm (MLFMA) formalism to model radiation and scattering by/from large planar microwave structures is presented. The technique relies on an electric field integral equation (EFIE) formulation and a series expansion for the Green dyadic, based on the use of perfectly matched layers (PML). In this way, a new PML-MLFMA is developed to efficiently evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. The computational complexity of the new algorithm scales down to O(N) for electrically large structures. The theory is validated by means of several illustrative, numerical examples.