Conventional Finite-difference Time-domain Research Articles

Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal

A discretization grid and its associated time-stepping formulas for a finite-difference time-domain method in a nonorthogonal coordinate system are introduced to simulate electromagnetic wave propagation and scattering. The method is applied to compute the band structure of a photonic crystal with a skew lattice. Unlike the conventional finite-difference time-domain method in a nonorthogonal coordinate system, the present method can treat discontinuities in the material parameters appropriately and thus does not have any problem of numerical instability.

Stability of symplectic finite-difference time-domain methods

Problems with slowly varying electromagnetic fields may be difficult to treat using finite-difference time-domain (FDTD) method. FDTD method was extended to symplectic FDTD methods to resolve the problems. Stability of schemes is a key to the efficient calculation of these problems. The stability of newly developed symplectic FDTD methods is examined. The developed symplectic FDTD methods show better stability than the conventional FDTD method.

The Effective Analysis of Electromagnetic Bandgap Structure of E-Uniplane Corrugated in a Rectangular Waveguide By the Fdtd of Wave Equation At Ka-Band

An effective analysis of electromagnetic bandgap structure of E-uniplane corrugated rectangular waveguide by the finite difference time domain (FDTD) of wave equation is presented in this paper. It is demonstrated that the presented method is effective by the good agreement between the data obtained from the conventional FDTD and ones from our presented. The characteristics of the E-uniplane corrugated waveguide show that both very wide selectable stop-band and pass-band are available when the parameters of the ripples are changed.

Modal MRTD approaches for the efficient analysis of waveguide discontinuities

This paper, the multi-resolution time-domain (MRTD) technique is applied to the waveguide discontinuity problem for fast-scattering parameter computation. To improve the computational efficiency, both three-dimensional (3-D) waveguide regions, including discontinuities, and one dimensional (1-D) homogeneous waveguide region, terminated with the modal absorbing boundary condition (ABC), are simulated in the wavelet domain with the mode composition/expansion algorithm from the modal analysis. A WG-90 rectangular waveguide with a thick asymmetric iris is analyzed and the numerical results are compared with conventional finite-difference time-domain (FDTD) results and mode-matching results.

Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method

This paper presents a comprehensive analysis of numerical dispersion of the recently developed unconditionally stable three-dimensional finite-difference time-domain (FDTD) method where the alternating-direction-implicit technique is applied. The dispersion relation is derived analytically and the effects of spatial and temporal steps on the numerical dispersion are investigated. It is found that the unconditionally stable FDTD scheme has advantages over the conventional FDTD of the Yee's scheme in modeling structures of fine geometry where a graded mesh is required. The unconditionally stable FDTD allows the use of a large time step in a region of fine meshes while maintaining numerical dispersion errors smaller than those associated with the region of coarse meshes.

Time-domain wavelet Galerkin modeling of two-dimensional electrically large dielectric waveguides

The time-domain wavelet-Galerkin method based on Daubechies' compactly supported scaling functions of high regularity has been applied to the analysis of two-dimensional dielectric slab waveguides that have typical dimensions and material parameters of optical integrated waveguide components, and the results are compared with those obtained with the conventional finite-difference time-domain method. It has been found that the proposed method allows discretization with a much coarser grid than the conventional time-domain analysis techniques due to its local sampling and highly linear numerical dispersion properties. A series of numerical experiments demonstrates the capability of the method to simulate the wave propagation of electrically large inhomogeneous media with reduced computational expenditure.

Numerical simulation of microstrip resonators and filters using the ADI-FDTD method

In this paper, we derived the characteristics of typical and practical microstrip components such as microstrip linear resonators and microstrip low-pass filters using the alternating-direction-implicit-finite-difference-time-domain (ADI-FDTD) method to examine the calculation accuracy and efficiency of the method. The resonators and the filters included very narrow gaps and strips, respectively. In this case, very fine cells must be applied there for the finite-difference time-domain (FDTD) modeling. In the conventional FDTD method, fine cells cause a reduction of the time-step size because of the Courant-Friedrich-Levy (CFL) stability condition, which results in an increase in calculation time. In the ADI-FDTD method, on the other hand, a larger time-step size than the CFL stability condition limitation could be set. We compared the results of the ADI-FDTD method for various time-step sizes with the results of the conventional FDTD method and measured data.

Scaling-function based multiresolution time domain analysis for planar printed millimetre-wave integrated circuits

The paper applies a scaling-function based multiresolution time domain (MRTD) scheme, in conjunction with an anisotropic perfectly matched layer (APML) for open and PEC-shielded boundary truncations, to analyse various planar millimetre-wave integrated circuits (MICs). Although adding complexity in deriving update equations and extracting MIC characteristics compared with the conventional finite difference time domain (FDTD) method, the MRTD scheme does provide a systematic, constructive, and flexible tool for the analysis of practical planar printed MIC structures. In particular, it is shown that the MRTD scheme is very efficient and requires only about 15% of the computational space and 25% or less of the time needed for the conventional FDTD techniques for all structures investigated in this research.

Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained.

A hybrid 2-D ADI-FDTD subgridding scheme for modeling on-chip interconnects

This paper presents a novel technique for extracting the propagation characteristics of on-chip interconnects. A hybrid two-dimensional subgridding scheme, based on a combination of the finite-difference time-domain (FDTD) method and the alternating-direction implicit (ADI-)FDTD technique, is utilized. The ADI-FDTD scheme is used for fine grid in the vicinity of the metallic etch, while the coarse FDTD grid is used outside this region. The advantage of the ADI-FDTD scheme is that it can be synchronized with the time marching step employed in the coarse FDTD scheme, obviating the need for the temporal interpolation of the fields in the process. This helps to render the hybrid ADI-FDTD subgridding scheme to be more efficient than the conventional FDTD subgridding algorithm in terms of the run time. The phase and attenuation constants of the dominant mode of a lossy stripline are computed by the proposed scheme to validate the technique.

Hybrid finite-difference/finite-volume time-domain analysis for microwave integrated circuits with curved PEC surfaces using a nonuniform 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.

Partially prism-gridded FDTD analysis for layered structures of transversely curved boundary

In this paper, a partially prism-gridded finite-difference time-domain (FDTD) method is proposed for the analysis of practical microwave and millimeter-wave planar circuits. The method is featured by hybridizing the flexible prism-based finite-element method to handle the region near the curved metallization boundary and the efficient rectangular-gridded FDTD method for most of the regular region. It can be used to deal with shielded or unshielded planar components such as patch antennas, filters, resonators, couplers, dividers, vias, and various transitions between planar transmission lines. Although only representative structures, e.g., grounded via, through hole via, and coplanar waveguide to coplanar stripline transition, are analyzed in this paper, the underlined formulation is applicable to layered structures with arbitrary curved boundary in the transverse direction. The accuracy of this method is verified by comparing the calculated results with those by other methods. Also, by the analysis of computational complexity, the present method is shown to be as efficient as the conventional FDTD method, with negligible overhead in memory and computation time for handling the curved boundary.

FDTD analysis of microwave hearing effect

This paper presents a numerical analysis of the thermoelastic waves excited by the absorbed energy of pulsed microwaves in a human head. First, the authors calculate the distribution of the specific absorption rate using a conventional finite-difference time-domain (FDTD) algorithm for the Maxwell's equation. They then calculate the elastic waves excited by the absorbed microwave energy. The FDTD method is again applied to solve the elastic-wave equations. The validity of the analysis for elastic waves is confirmed through comparison of the FDTD results with the analytical solutions in a sphere model. Two anatomically based human head models are employed for numerical calculations. The waveforms of the calculated pressure waves are different from the previously reported ones. It is especially shown that the surface heating is important in exciting the fundamental mode of the pressure waves in the head. The pulsewidth dependency of the loudness of microwave hearing is clearly explained by the simulation with realistic head models. The peak pressure of elastic waves in the realistic head models is of the same order as the previously reported values obtained with a homogeneous sphere model. The strength of elastic wave is discussed in consideration of the safety of this phenomenon.

A generalized methodology based on higher-order conventional and non-standard FDTD concepts for the systematic development of enhanced dispersionless wide-angle absorbing perfectly matched layers

A generalized theory of higher-order finite-difference time-domain (FDTD) schemes for the construction of new dispersionless Berenger and Maxwellian unsplit-field perfectly matched layers (PMLs), is presented in this paper. The technique incorporates both conventional and non-standard approximating concepts. Superior accuracy and modelling attributes are further attained by biasing the FDTD increments on generalizations of Padé formulae and derivative definitions. For the inevitably widened spatial stencils, we adopt the compact operators procedure, whereas temporal integration is alternatively performed via the four-stage Runge–Kutta integrator. In order to terminate the PML outer boundaries and decrease the absorber's necessary thickness, various higher-order lossy absorbing boundary conditions (ABCs) are implemented. Based on the previous theory, we finally introduce an enhanced reflection-annihilating PML for wide-angle absorption. The novel unsplit-field PML has a non-diagonal symmetric complex tensor anisotropy and by an appropriate choice of its parameters together with new conductivity profiles, it can successfully absorb waves of grazing incidence, thus allowing its imposition much closer to electrically large structures. Numerical results reveal that the proposed 2- and 3-D PMLs suppress dispersion and anisotropy errors, alleviate the near-grazing incidence effect and achieve significant savings in the overall computational resources. Copyright © 2000 John Wiley & Sons, Ltd.

On the solution of a class of large body problems with full or partial circular symmetry by using the finite-difference time-domain (FDTD) method

This paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry. The method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem. It does so by dividing the problem into two parts: a larger 3-D region with circular symmetry, and a smaller 2-D region without circular symmetry. An finite-difference time-domain (FDTD) algorithm is used to analyze the circularly symmetric 3-D case, while a method of moments (MoM) code is employed for the nonsymmetric part of the structure. The results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system. The advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2-D as opposed to a full 3-D FDTD simulation. In addition to enhancing computational efficiency, the FDTD algorithm used in this paper also features one improvement over conventional FDTD methods: a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces. The accuracy of the method is validated via a comparison of simulated and measured results.

A new algorithm for the incorporation of arbitrary linear lumped networks into FDTD simulators

The inclusion of lumped elements, both linear and nonlinear, into the finite-difference time-domain (FDTD) algorithm has been recently made possible by the introduction of the lumped element FDTD method. Such a method, however, cannot efficiently and accurately account for two-terminal networks made of several lumped elements, arbitrarily connected together. This limitation can be removed as proposed in this paper by describing the network in terms of its impedance in the Laplace domain and by using appropriate digital signal-processing methodologies to fit the resulting description to Yee's algorithm. The resulting difference equations allow an arbitrary two-terminal network to be inserted into one FDTD cell, preserving the full explicit nature of the conventional FDTD scheme and requiring a minimum number of additional storage variables. The new approach has been validated by comparison with the exact solution of a parallel-plate waveguide loaded with lumped networks in the transverse plane.

A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling

A hybrid implicit-explicit finite-difference time-domain (FDTD) method for solving the wave equation in nonlinear optical waveguiding structures is proposed. The new scheme combines the computational simplicity of the explicit scheme in linear medium regions with the superior stability property of the partially implicit scheme in regions of nonlinear materials, thus eliminating potential problems of instability associated with nonlinearity. Simulation results for Kerr-type nonlinear slab waveguides and corrugated waveguides are presented and compared with those obtained using the conventional noniterative FDTD scheme.

MRTD analysis of a transient electromagnetic pulse propagating through a dielectric layer

On the basis of a scaling function based multiresolution time domain (MRTD) scheme, we analyse a transient electromagnetic pulse propagating through a dielectric layer in conjunction with an anisotropic perfectly matched layer (APML) for mesh truncation. Herein we have carefully investigated three different cases including TEM x , TE z and TM z waves that are normally incident on an open or PEC parallel-plate bounded propagation system. Purposely, we employ a similar notation in formulations to that applied in the conventional finite difference time-domain (FDTD) method for their comparison, rather than using the state-space representation. It is found that the computed reflected coefficients for all configurations are in good agreement with those obtained with the FDTD and analytic methods, while its corresponding requirement on computational memory and CPU time is considerably reduced.

A nonuniform cylindrical FDTD algorithm with improved PML and quasi-PML absorbing boundary conditions

Many applications require time-domain solutions of Maxwell's equations in inhomogeneous, conductive media involving cylindrical geometries with both electrically small and large structures. The conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid will result in a staircasing error, and wastes many unnecessary cells in regions with large structures in order to accommodate the accurate geometrical representation in regions with small structures. In this work, an explicit FDTD method with a nonuniform cylindrical grid is developed for time-domain Maxwell's equations. A refined lattice is used near sharp edges and within fine geometrical details, while a larger lattice is used outside these regions. This provides an efficient use of limited computer memory and computation time. The authors use two absorbing boundary conditions to a nonuniform cylindrical grid: (1) the straightforward extension of Berenger's perfectly matched layer (PML) which is no longer perfectly matched for cylindrical interfaces, thus the name quasi-PML, (QPML); (2) the improved true PML based on complex coordinates. In practice, both PML schemes can provide a satisfactory absorbing boundary condition. Numerical results are shown to compare the two absorbing boundary conditions (ABCs) and to demonstrate the effectiveness of the nonuniform grid and the absorbing boundary conditions.

A finite-difference time-domain method without the Courant stability conditions

In this paper, a finite-difference time-domain method that is free of the constraint of the Courant stability condition is presented for solving electromagnetic problems. In it, the alternating direction implicit (ADI) technique is applied in formulating the finite-difference time-domain (FDTD) algorithm. Although the resulting formulations are computationally more complicated than the conventional FDTD, the proposed FDTD is very appealing since the time step used in the simulation is no longer restricted by stability but by accuracy. As a result, computation speed can be improved. It is found that the number of iterations with the proposed FDTD can be at least three times less than that with the conventional FDTD with the same numerical accuracy.