Nonuniform Finite-difference Time-domain Research Articles

Efficient Parallel FDTD Method Based on Non-Uniform Conformal Mesh

The finite-difference time-domain (FDTD) method is a versatile electromagnetic simulation technique, widely used for solving various broadband problems. However, when dealing with complex structures and large dimensions, especially when applying perfectly matched layer (PML) absorbing boundaries, tremendous computational burdens will occur. To reduce the computational time and memory, this paper presents a Message Passing Interface (MPI) parallel scheme based on non-uniform conformal FDTD, which is suitable for convolutional perfectly matched layer (CPML) absorbing boundaries, and adopts a domain decomposition approach, dividing the entire computational domain into several subdomains. More importantly, only one magnetic field exchange is required during the iterations, and the electric field update is divided into internal and external parts, facilitating the synchronous communication of magnetic fields between adjacent subdomains and internal electric field updates. Finally, unmanned helicopters, helical antennas, 100-period folded waveguides, and 16 × 16 phased array antennas are designed to verify the accuracy and efficiency of the algorithm. Moreover, we conducted parallel tests on a supercomputing platform, showing its satisfactory reduction in computational time and excellent parallel efficiency.

Nonuniform and Higher-order FDTD Methods for the Schrödinger Equation

Two Finite-Difference Time-Domain (FDTD) methods are developed for solving the Schrödinger equation on nonuniform tensor-product grids. The first is an extension of the standard second-order accurate spatial differencing scheme on uniform grids to nonuniform grids, whereas the second utilizes a higher-order accurate spatial scheme using an extended stencil. Based on discrete-time stability theory, an upper bound is derived for the time step of both proposed schemes. It is shown that the time step derived in this way can be larger compared to the known stability criterion. Furthermore, the numerical dispersion error is investigated as a function of the time step, the spatial step and the propagation direction. Numerical experiments are compared with analytical solutions and demonstrate the increased accuracy of the higher-order scheme as well as the advantageous properties of nonuniform gridding.

Hybrid FDTD–PE method for Loran‐C ASF prediction with near‐source complex topography

The parabolic equation (PE) method and finite-difference time-domain (FDTD) method are combined to predict long-range Loran-C additional secondary factors (ASFs) in situations with near-source complex topography. The non-uniform FDTD method is employed in the complex source region, while the PE method is used for propagation over smooth terrain to a long distance. By using the advantages of each algorithm, the hybrid FDTD-PE approach is capable of modelling the near-source topographic details, while saving much computational resources as compared to a full FDTD solution. Numerical results along several paths are used to validate the hybrid algorithm. Furthermore, the hybrid method is applied to analyse the effect of near-source topographic complexities, including non-flat land, land-sea transition, and island (cliff)-sea transition, on the navigational coverage for the planning of the Loran-C systems.

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank–Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit–Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications.

An Efficient Parallel 3-D FDTD Method for Calculating Lightning-Induced Disturbances on Overhead Lines in the Presence of Surge Arresters

In this paper, we propose an efficient modeling technique for incorporating surge arresters in finite-difference time-domain (FDTD) simulations of lightning-induced disturbances in power networks. Instead of using piecewise linear approximations for the V–I curve of an arrester, as usually done in the literature, we derive new updating equations for calculation of electric field components required at each FDTD time step. This is done in a semi-implicit manner where we first obtain a time-stepping relation of electric field based on the V–I curves of the arresters. The time-stepping relation in each time step is solved by the Newton–Raphson method to update the electric field components. The proposed technique is implemented into a nonuniform parallel FDTD code, which is used to simulate a three-phase distribution line of about 800 m equipped with lightning arresters and a neutral wire, installed at the International Center for Lightning Research and Testing at Camp Blanding Florida. The results of FDTD numerical simulations are found to be in excellent agreement with experimental data associated with triggered lightning.

Design and analysis of on‐package dual‐mode band pass filters for highly integrated wireless transceivers

AbstractIn this paper, various planar printed microwave bandpass filters (BPFs) are designed and analyzed by applying a nonuniform finite‐difference time‐domain (NU‐FDTD) method. These filters, referred to as integrated‐circuit package filters (ICPFs), are designed in such a way that they operate in dual mode (DM), that is, at TM and TM, to ensure a good electric performance at the center frequency. They operate at 2.4 and 5.25 GHz, which are the frequencies allocated to wireless local area networks (WLANs). The frequency characteristics in terms of the scattering parameters are taken for analysis, and the results are compared to the measurements as well as the computed results using High‐Frequency Structure Simulator (HFSS) software. The results show excellent agreement between the numerical and experimental data, and the proposed DM‐ICPF structures can be applied to on‐package highly integrated wireless transceiver systems. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 756–760, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21466

Design and analysis of integrated-circuit package antenna (ICPA) for dual-band wireless transceivers

This article presents study of a dual-band integrated-circuit package antenna (ICPA), which operates concurrently on dual bands at 2.4 and 5.25 GHz. The antenna is designed and printed on the top surface of an IC package and fed by a single coaxial line, while the transceiver is implemented on the opposite side of the package, through the separation of a common ground plate. This “cavity-down” arrangement minimizes the electromagnetic interference between the antenna and transceiver, and satisfies the miniaturization of the design. The study consists of numerical computations, which are performed through an in-house computer solver based on the nonuniform finite-difference time-domain (NU-FDTD) method and experimental measurements. Together with the data computed using the high-frequency structure simulator (HFSS) software, the results show excellent agreement between the numerical and experimental data, and the proposed structure is deemed as a useful application in the area of highly integrated wireless transceivers. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.

Studies of an On-Package Dual-Mode Square-Loop Band Pass Filter for Highly Integrated Wireless Transceivers Using NU-FDTD

An on-package dual-mode square-loop band pass filter is studied by applying a non-uniform finite difference time domain (NU-FDTD) method. The filter is integrated on a package containing a transceiver, and it is designed to operate in dual-modes, i.e., TM 2 100 and TM 2 010 , to ensure a good electric performance around the center frequency at 5.25 GHz, which is commonly allocated in wireless local area network (WLAN). This filter is also referred as a dual-mode integrated-circuit package filter (DM-ICPF) based on its operational mode and integration onto an IC-package. The frequency characteristics in terms of the scattering parameters are studied, and the results are validated against the computed results using commercial software, the high frequency structure simulator (HFSS). Results show an excellent agreement between the numerical data, and the proposed DM-ICPF structure can be applied in the area of the highly integrated wireless transceivers.

U-shaped planar inverted-F microstrip antenna with a U-shaped slot inset for dual-frequency mobile communications

This paper presents a novel configuration of a U-shaped, dual-frequency, single-feed, planar inverted-F microstrip antenna with a U-shaped slot (UU-PIFA). The antenna is well suited to telephone handsets used in today's mobile communication systems operating in both GSM and DCS 1800 bands, namely 0.9 and 1.8 GHz, respectively. An initial design is derived from an empirical approximation and a transmission line model of a rectangular microstrip antenna. The paper analyses, examines, and fine-tunes the electrical performance of the antenna, including the return loss, operating frequencies, bandwidths, input impedance, and far-field radiation patterns, by using the generalised non-uniform finite difference time domain (NU-FDTD) Maxwell solver. In addition, to increase the efficiency of the FDTD solver, the concept of domain decomposition is utilised, which enables one to eliminate redundant computational space, and thereby reduce the memory and CPU time requirements.

Application of the non-uniform FDTD algorithm on an auto-adjustable mesh to the analysis of scattering parameters of a sandwiched-type coplanar waveguide with adjacent vias in PCBs

In this paper, we analyse scattering parameters for a sandwiched-type coplanar waveguide (SCPW) with three pairs of vias that are adjacent to each other. The above structure is frequently encountered in printed circuit board (PCB) designs, and is analysed by using a non-uniform finite difference time domain (FDTD) algorithm on an auto-adjustable mesh. The mesh generator developed for this algorithm can efficiently generate the files for the geometry—as well as for the material parameters—that serve as the inputs to the non-uniform FDTD solver. In addition, the generator has numerous graphical functions that not only ensure accuracy of generated data files but also make them convenient for the user. We carry out an extensive parametric study and show that the S -parameters are very dependent on the geometrical parameters of the vias, especially at high frequencies.

A novel U-shaped planar microstrip antenna for dual-frequency mobile telephone communications

We present a novel configuration of a U-shaped dual-frequency single feeding port planar inverted-F microstrip antenna for mobile communication applications in both the GSM and DCS 1800 systems operated at 0.9 and 1.8 GHz, respectively. Starting from an initial design derived from an empiric approximation and transmission line model for a standard rectangular microstrip antenna, we analyze, tune, and optimize the electric performance of the antenna and its dimensions by means of the generalized nonuniform finite-difference time-domain (NU-FDTD) Maxwell's solver.

Analysis of diffractive optical elements using a nonuniform finite-difference time-domain method

We present the analysis of diffractive optical elements (DOEs) using a two-dimensional nonuniform finite-difference time- domain (FDTD) method. Because the feature sizes in a DOE profile are in general irregular, their analysis using a conventional formulation of the FDTD, i.e., a uniform orthogonal grid, typically requires a high spatial sampling. This in turn raises the computational time and memory requirements for analysis. However, by using a nonuniform grid configuration one can more accurately represent the computation boundary of the DOE, and consequently reduce computational costs. To this end we apply our method to the analysis of both multilevel and subwavelength DOEs to illustrate its utility.

Finite-difference time-domain analysis of a stacked dual-frequency microstrip planar inverted-F antenna for mobile telephone handsets

We describe a stacked, dual-frequency microstrip planar inverted-F antenna (DF-PIFA) for mobile telephone handsets that can concurrently work in two frequency-bands, viz., those associated with the GSM and DCS 1800 systems operating at 0.9 GHz and 1.8 GHz, respectively. The proposed microstrip DF-PIFA is fed by a coaxial line, as opposed to two separated feed lines used in the conventional design. The design is carried out in a systematic manner and involves two steps. We begin with an initial configuration of the PIFA that is based on a standard design for a microstrip patch antenna fed by a coaxial line and is derived from an empirical approximation in conjunction with a transmission line model. Next, we employ a computer-aided design (CAD) tool, based on the nonuniform finite-difference time-domain (NU-FDTD) Maxwell solver, to optimize the performance characteristics of the DF-PIFA, including the return loss, the matching of the input impedance, and the far-field radiation patterns.

Application of the nonuniform FDTD technique to analysis of coaxial discontinuity structures

In this paper, we employ the nonuniform finite-difference time-domain (NUFDTD) technique to accurately model discontinues in complex coaxial configurations. We take advantage of the azimuthal symmetry of the structure to reduce the original problem into an equivalent two-dimensional one, and we do this by projecting the three-dimensional Yee cell onto two-dimensional planes. Numerical results are presented for various discontinuities to illustrate the application of the method. We show that the NUFDTD technique yields results that are in excellent agreement with the mode-matching method.

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.

Extending PML absorbing boundary condition to truncate microstrip line in nonuniform 3D FDTD grid

The Berenger's perfectly matched layer (PML) absorbing boundary condition is applied to terminate a microstrip line with metal strip and multilayer dielectric media extending into the PML regions. In order to handle the inhomogeneous properties of the PML layers better, the integral form of the Maxwell's equations, approximated by central-difference expressions instead of exponential-difference expressions, are utilized to deduce the finite-difference time-domain (FDTD) equations for updating field components inside PML media. The derived formulas are proven to be flexible and convenient for generating and handling the PML layers in a nonuniform FDTD grid. Simulation results show that the proposed multilayer PML boundary condition can effectively absorb the outgoing wave with at least -80-dB reflection coefficient under a complicated boundary situation.

AutoMesh: an automatically adjustable, nonuniform, orthogonal FDTD mesh generator

In this article, we introduce a three-dimensional, automatically adjustable, non-uniform orthogonal-mesh generator, AutoMesh, developed using a Windows application-development package, Microsoft Visual Basic. The developed mesh-generating package can efficiently produce geometrical and material data files for a complex electromagnetic configuration that serve as inputs to a generalized non-uniform finite-difference time-domain (FDTD) Maxwell's equations solver. In addition, the fruitful graphical functions of the package insure not only the accuracy of the generated data files, but also the ease of mesh generation for complex objects. Herein, we first present the algorithm of mesh generation, and then illustrate graphical features of the package.

A technique for improving the accuracy of the nonuniform finite-difference time-domain algorithm

This paper deals with the problem of improving the accuracy of the nonuniform finite-difference time-domain (NUFDTD) algorithm, which is known to contain higher discretization errors than the conventional uniform FDTD. The improvement is achieved by effectively canceling out the numerical reflections that typically occur due to dispersion in the nonuniform mesh. The modified nonuniform algorithm is applied to a generic coaxial discontinuity problem and to that of near-to-far-field transformation. The proposed method is simple, does not require any interpolations or extrapolations, provides higher accuracy than the conventional NUFDTD algorithm, and is stable.

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 nonuniform FDTD technique for efficient analysis of propagation characteristics of optical-fiber waveguides

In this paper, we present a highly efficient one-dimensional cylindrical nonuniform finite-difference time-domain (1-D CNUFDTD) method, which utilizes the unsplit anisotropic perfectly matched layer (APML) for mesh truncation along the radial direction to analyze axisymmetric optical-fiber waveguides. As a first step, we validate the proposed FDTD algorithm by analyzing a uniform dielectric waveguide of circular cross section and show that the results are in excellent agreement with the conventional mode theory solutions. Next, we apply the algorithm to analyze propagation characteristics of a number of commonly used optical-fiber waveguides, i.e., step-index multimode, graded-index multimode, and single-mode step-index configurations.