Hybrid finite-volume finite-difference time-domain modelling ofcurved surfaces

A computationally efficient hybrid finite-volume finite-difference time-domain (FV-FDTD) method is proposed to model the scattering from curved objects. The hybrid FV-FDTD method uses a local conforming mesh consisting of only two FVTD cells, one either side of the scatterer's contour, giving a better approximation to the surface. The improved definition of the scatterer using the hybrid FV-FDTD method is shown to improve the solution in comparison to the FDTD method     

A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions

A systematic conformal finite-difference time-domain (FDTD) algorithm for the direct modeling of dielectric interfaces in three dimensions is presented in this paper. The straightforward procedure is based on the proper reformation of the grid cells in the vicinity of the dielectric surface, leading thus to the creation of five-faced prisms on the primary grid, apart from the standard hexagonal ones. The new scheme overcomes any topological deficiency that forbids the contour path FDTD and conformal FDTD technique to directly simulate dielectric boundaries, since it maintains the lattice duality. Therefore, no instabilities, even late-time ones, are observed. On the other hand, the accuracy obtained, even with very coarse meshes, is very good as is proved by the numerical analysis of various resonance problems.     

Hybrid finite-difference/finite-volume time-domain analysis formicrowave integrated circuits with curved PEC surfaces using anonuniform rectangular grid

In this paper, we present a hybrid algorithm that combines the finite-difference time-domain (FDTD) and finite-volume time-domain (FVTD) methods to analyze microwave integrated-circuit structures that may contain curved perfect electric conductor (PEC) surfaces. We employ the conventional nonuniform FDTD in regions where the objects are describable with a rectangular mesh, while applying the FVTD method elsewhere where we need to deal with curved PEC configurations. Both the FDTD and FVTD quantities are defined in the mutually overlapping regions, and these fields from the respective regions are interpolated by using their nearest neighbors. We validate this algorithm by analyzing the scattering parameters of a stripline with one or more adjacent cylindrical vias, whose geometries are frequently encountered in printed-circuit-board designs. It is found that the hybrid FDTD-FVTD approach requires little increase in central processing unit time and memory in comparison to the conventional FDTD, while its computational accuracy is significantly improved over a wide range of frequencies. Specifically, this accuracy is found to be comparable to that achieved by doubling the mesh density of the staircased FDTD     

The advantages of triangular and tetrahedral edge elements forelectromagnetic modeling with the finite-element method

In this paper, we examine the numerical dispersion properties of the tetrahedral edge element in comparison to other edge and nodal elements. For all nodal elements as well as hexahedral edge elements, the phase error is always either positive or negative for waves propagating at any incidence angle, which means that the error accumulates as the wave propagates from element to element. This effect can produce large errors for electrically large geometries. On the other hand, the tetrahedral edge elements can produce either a negative or positive phase error, depending on the direction of propagation through the element. For an unstructured mesh, phase cancellation occurs since the orientation of the tetrahedral elements are arbitrary. Because of the cancellation, the numerical dispersion error is very low for meshes composed of well-shaped tetrahedral edge elements. Numerical results are presented to demonstrate this point     

Analysis of edge slots in rectangular waveguide using finite-difference time-domain method

A finite-difference time-domain (FD-TD) method for analysing edge slots in rectangular waveguides is suggested. The proposal is supported by an example.<>     

Finite-difference time-domain modeling of curved surfaces [EMscattering]

The finite-difference-time-domain (FDTD) method is generalized to include the accurate modeling of curved surfaces. This generalization, the contour path CP), method, accurately models the illumination of bodies with curved surfaces, yet retains the ability to model corners and edges. CP modeling of two-dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented     

Analysis of curved and angled surfaces on a Cartesian mesh using anovel finite-difference time-domain algorithm

The widely accepted finite-difference time-domain algorithm, based on a Cartesian mesh, is unable to rigorously model the curved surfaces which arise in many engineering applications, while more rigorous solution algorithms are inevitably considerably more computationally intensive. A nonintensive, but still rigorous, alternative to this approach has been to incorporate a priori knowledge of the behavior of the fields (their asymptotic static field solutions) into the FDTD algorithm. Unfortunately, until now, this method has often resulted in instability. In this contribution an algorithm (denoted `SFDTD' for second-order finite difference time domain) is presented which uses the static field solution technique to accurately characterize curved and angled metallic boundaries. A hitherto unpublished stability theory for this algorithm, relying on principles of energy conservation, is described and it is found that for the first time a priori knowledge of the field distribution can be incorporated into the algorithm with no possibility of instability. The accuracy of the SFDTD algorithm is compared to that of the standard FDTD method by means of two test structures for which analytic results are available     

BI-FDTD: a novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media

This paper presents a newly developed finite-difference time-domain (FDTD) technique, referred to as BI-FDTD, for modeling electromagnetic wave interactions with bi-isotropic (BI) media. The theoretical foundation for the BI-FDTD method will be developed based on a wavefield decomposition. The main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium, which makes it possible to readily apply conventional FDTD analysis techniques. The BI-FDTD scheme will also be extended to include the dispersive nature of chiral media, an important subclass of bi-isotropic media. This extension represents the first of its kind in the FDTD community. Validations of this new model are demonstrated for a chiral half-space and a chiral slab.     

Design of dual-polarised multiband frequency selective surfacesusing fractal elements

A technique is proposed for the design of multiband frequency selective surfaces (FSSs) that is based on the use of fractal screen elements. The authors demonstrate the design methodology by exploiting the self-similarity of the crossbar fractal to implement a tri-band FSS. Another benefit of this design approach, in addition to its multiband performance, is that the frequency response of both the TE and TM modes are exactly the same, owing to the symmetry in the tree-like fractal structure of the screen elements. Dielectric loading effects have been considered for practical implementation of designs with coverage exceeding two bands. Finally, it is noted that the locations of the individual bands can be controlled by the scaling or similarity factor used in the construction of the fractal screen elements     

A selective survey of the finite-difference time-domain literature

The finite-difference time-domain (FDTD) method is arguably the most popular numerical method for the solution of problems in electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. Furthermore, extensions and enhancements to the method are continually being published, which further broaden its appeal. Because of the tremendous amount of FDTD-related research activity, tracking the FDTD literature can be a daunting task. We present a selective survey of FDTD publications. This survey presents some of the significant works that made the FDTD method so popular, and tracks its development up to the present-day state-of-the-art in several areas. An “on-line” BibT_EX database, which contains bibliographic information about many FDTD publications, is also presented     

Reduced-order modeling of multiscreen frequency-selective surfacesusing Krylov-based rational interpolation

A method is presented for generating a broad-band rational interpolant approximation of the reflection coefficient of multiple-screen frequency-selective surfaces (FSSs). The technique is structured around a linearization of the system provided by a spectral domain moment method-based analysis of the FSS, followed by a model-order reduction of the linearized system using the dual rational Arnoldi method. This process creates a rational interpolant of the linearized system that matches its transfer function and its derivatives at several expansion points in the Laplace domain. Numerical results indicate that a reduced-order model with a system matrix of dimension less than 20×20 can accurately reproduce the broad-band behavior of multiscreen FSSs originally modeled with several hundreds or thousands of unknowns     

Faster finite-difference time-domain method using moving spatial boundaries

The finite-difference time-domain (FD-TD) method is augmented with the moving spatial boundaries which define the computation domain. In cases where the simulated electromagnetic field is zero for some time over part of the spatial domain studied, savings in computation time can be realised. Saving of 50 and 25% have been achieved for transmission and reflection analyses, respectively, in an example concerning a coplanar waveguide.<>     

Thin sheet modeling using shell elements in the finite-element time-domain method

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this paper, the focus is on modeling of thin material sheets and coatings in the finite-element time-domain method. The proposed method is based on degenerated prism elements, so-called shell elements. For a dielectric sheet the thickness is assumed small compared to the wavelength for all frequencies of interest. An important characteristic of the method is that it takes the discontinuity of the normal electric field component at a dielectric interface into account. The accuracy of the method is demonstrated for three different scattering cases. Comparisons are made with analytical data and results obtained on grids for which the thickness of the sheets is resolved. Good agreement is observed in all cases.     

A frequency-dependent finite-difference time-domain formulation forgeneral dispersive media

A weakness of the finite-difference-time-domain (FDTD) method is that dispersion of the dielectric properties of the scattering/absorbing body is often ignored and frequency-independent properties are generally taken. While this is not a disadvantage for CW or narrowband irradiation, the results thus obtained may be highly erroneous for short pulses where ultrawide bandwidths are involved. In some recent publications, procedures based on a convolution integral describing D(t) in terms of E(t) are given for media for which the complex permittivity ∈*(ω) may be described by a single-order Debye relaxation equation or a modified version thereof. Procedures are, however, needed for general dispersive media for which ∈*(ω) and μ*(ω) may be expressible in terms of rational functions, or for human tissues for which multiterm Debye relaxation equations must generally be used. The authors describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) in terms of E(t) by means of a differential equation involving E, and their time derivatives. The method is illustrated for several examples     

Treating late-time instability of hybridfinite-element/finite-difference time-domain method

The hybrid finite element/finite-difference time-domain (FETD/FDTD) method previously proposed to handle arbitrarily shaped dielectric objects is employed to investigate electromagnetic problems of high Q systems for which the transient response over a very long duration is necessary. To begin with, the paper demonstrates that this hybrid method may suffer from late-time instability and spurious DC modes. Then an approach which combines the temporal filtering and frequency shifting techniques is presented to overcome sequentially and, respectively, the two drawbacks. Its accuracy is validated by the favorable comparison with several different methods for the analysis of resonant frequencies and and factors of the various modes in an isolated dielectric resonator. Finally, the present method is applied to calculate the scattering parameters on the microstrip line due to the presence of the cylindrical dielectric resonator     

A MATLAB-based transmission-line virtual tool: finite-difference time-domain reflectometer

This article introduces a simple virtual tool, TDRMeter, for the investigation and visualization of time-domain pulsed voltage/current, traveling along a terminated finite-length transmission line, without and with faults somewhere between the source and the load. The package can be used as an educational tool in various undergraduate lectures to aid in teaching electromagnetics as well as transmission lines.     

Steady-state response by finite-difference time-domain method and lanczos algorithm

A hybrid method combining the finite-difference time-domain (FDTD) method and Lanczos algorithm is proposed for efficiently obtaining the steady-state response for closed systems. With the Lanczos algorithm, modes of the FDTD operator can be easily extracted to reconstruct the steady-state response at any time by an analytic formula. With the aid of the time-reversal technique, existing FDTD codes are preserved. Numerical results show that with only very few Lanczos iterations, results of good agreement can be achieved between the proposed method and brute-force FDTD.     

Staircase-free finite-difference time-domain formulation forgeneral materials in complex geometries

A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee (1966) scheme for complex geometries since the computational representation of physical structures is not of a staircased nature. Furthermore, electromagnetic boundary conditions are correctly enforced. The method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry. Both perfect electric conductors and dielectric structures have been investigated. Numerical results are presented and discussed     

A frequency-dependent finite-difference time-domain formulation fortransient propagation in plasma

Previous FDTD (finite-difference time-domain) formulations were not capable of analyzing plasmas for two reasons. First, FDTD requires that at each time step the permittivity and conductivity be specified as constants that do not depend on frequency, while even for the simplest plasmas these parameters vary with frequency. Second, the permittivity of a plasma can be negative, which can cause terms in FDTD expressions to become singular. A novel FDTD formulation for frequency-dependent materials (FD)²TD has been developed. It is shown that (FD) ²TD can be applied to compute transient propagation in plasma when the plasma can be characterized by a complex frequency-dependent permittivity. While the computational example presented is for a pulse normally incident on an isotropic plasma slab, the (FD)²TD formulation is fully three-dimensional. It can accommodate arbitrary transient excitation, with the limitation that the excitation pulse must have no zero frequency energy component. Time-varying electron densities and/or collision frequencies could also be included. The formulation presented is for an isotropic plasma, but extension to anisotropic plasma should be fairly straightforward     

Characterization of three-dimensional open dielectric structuresusing the finite-difference time-domain method

Millimeter and submillimeter wave three-dimensional (3-D) open dielectric structures are characterized using the finite-difference time-domain (FDTD) technique. The use of FDTD method allows for the accurate characterization of these components in a very wide frequency range. The first structure characterized through FDTD for validation purposes is a mm-wave image guide coupler. The derived theoretical results for this structure are compared to experimental data and show good agreement. Following this validation, a sub-mm wave transition from a strip-ridge line to a layered ridge dielectric waveguide (LRDW) in open environment is analyzed, and the effects of parasitic radiation on electrical performance are studied. The transition is found to be very efficient over a wide sub-mm frequency band which makes it useful for a variety of applications. In addition to the transition, a sub-mm wave distributed directional coupler made of the LRDW is extensively studied using the FDTD method as an analysis tool. Furthermore, an iterative procedure based on the FDTD models is used to design a 3-dB coupler with a center frequency of 650 GHz and negligible radiation loss. This successful design shows that the FDTD technique can be used not only as an analysis method, but also as a design tool to provide designs which take into account all high frequency parasitic effects