Finite-difference Time-domain Cell Research Articles

Switched boundary condition (XBC) in FDTD

A new type of boundary condition is introduced in the letter that takes advantage of nonstationary terminations of the finite-difference time-domain (FDTD) mesh. Three techniques are combined to achieve low cost absorbing boundary conditions with excellent properties: frequency up-conversion, inherent FDTD property of dissipation of energy at frequencies close to Nyquist limit, and semi-transparent wall to trap high frequency energy traveling away from the boundary at cell diagonals. The boundary achieves very high absorption levels within two to three FDTD cells. The performance of the boundary is tested in a rectangular waveguide. The goal of this research is to open up a new direction in absorbing boundary research that can lead to efficient absorption with very low memory and numerical costs.

An alternative approach to FD-TD analysis of magnetized ferrites

This paper presents a new approach to the finite difference-time domain (FD-TD) analysis of magnetized ferrites. An equivalent lumped circuit of an FD-TD cell filled with such a medium is developed. Then the lumped circuit is used to propose a new FD-TD algorithm. This algorithm is verified on canonical examples and is shown to be simple, accurate, robust and computationally more effective than the previously published approaches.

An improved formalism for FDTD analysis of thin-slot problems by conformal mapping technique

An improved expression of the thin-slot formalism has been proposed to alleviate the gridding of the finite-difference time-domain (FDTD) solution for electromagnetic problems involving narrow slots. By applying the conformal mapping technique, the varying field distribution near the slots is analytically derived and fully cast into a unit FDTD cell with effective permittivity and permeability. As a result, this formalism permits narrow slots to be modeled without reducing spatial grid size, even when the slot gap width is much smaller than a one space grid. The method has been applied to several transmission line problems and the results are compared with traditional FDTD and other thin-slot formalisms. It is verified that the proposed method is easy to implement, numerically efficient, and accurate.

Semi-empirical modeling of apertures for shielding effectiveness simulations

A novel method to include models of complex apertures into the finite-difference time-domain (FDTD) method is presented. Instead of resolving the geometrical details of the aperture, the aperture is treated as a magnetic dipole. The properties of the magnetic dipole moment are determined using the measured transmission cross section of the aperture. This semi-empirical model permits inclusion of complex apertures in FDTD simulations where the smallest dimension of the aperture is only a fraction of the FDTD cell size. Two types of complex apertures positioned in the top panel of a realistic enclosure have been modeled using the semi-empirical model in FDTD. Comparisons between simulated and measured shielding effectiveness of the enclosure are presented, and the results show that complex apertures can indeed be represented by simple magnetic dipoles in shielding effectiveness simulations.

Analysis of circular waveguide filter using enhanced FDTD

AbstractThe finite difference time domain (FDTD) analysis of iris‐coupled circular waveguide filters presents several challenges because they contain curved metal surfaces and electrically small slots. In this contribution it is shown that by enhancing the basic FDTD algorithm in three ways, filters of this type may be accurately characterized without the need for a highly dense mesh. The enhancements are: (i) an existing locally conformal mesh algorithm to model the curved metal surface, (ii) novel empirical correction factors to account for the singular field behaviour near the slots and their exact position relative to the FDTD cells and (iii) compensation for the numerical dispersion in the FDTD algorithm. The calculation of the correction factors and the implementation of the technique is discussed and the extent to which each of these three enhancements contributes to the reduction of numerical error is shown. In addition, it is shown that a novel combination (i) and (ii) leads to a robust and effective method of treating metal edges which are offset from the edges of the cells. The improvement obtained for a complete filter is demonstrated by comparison to measured results. Copyright © 2002 John Wiley & Sons, Ltd.

Two-dimensional finite difference time domain analysis of cylindrical transmission lines

Recently, there has been a growing interest in the use of cylindrical transmission lines in a variety of applications. In this paper, the finite difference time domain (FDTD) method is used to calculate the propagation characteristics of cylindrical transmission lines. An efficient two-dimensional (2D) FDTD algorithm is developed by projecting the three-dimensional FDTD cell in the cylindrical coordinates on to the r−φ plane. An effective absorbing boundary condition is employed to truncate the mesh at its outer radial boundary. In addition to a detailed description of the developed 2D-FDTD algorithm, extensive numerical results are derived for different cylindrical transmission lines and compared with data available in the literature. Specifically, the newly proposed cylindrical coplanar waveguide is studied both theoretically and experimentally.

Reduction of numerical dispersion in FDTD method through artificial anisotropy

In this paper, a simple and computationally low-cost modification of the standard finite-difference time-domain (FDTD) algorithm is presented to reduce numerical dispersion in the algorithm. Both two- and three-dimensional cases are considered. It is shown that the maximum error in phase velocity can be reduced by a factor of 2-7, depending on the shape of the FDTD cell. Although the reduction procedure is optimal for only single frequency, numerical examples show that the proposed method can also improve the accuracy significantly in wide-band inhomogeneous problems.

Exact global boundary condition with reduced computational complexity for grid truncation in acoustic finite difference time domain simulations

The numerical analysis of transient acoustic radiation by and scattering from inhomogeneous bodies is often carried out using the finite difference time domain (FDTD) method. However, FDTD grids must be truncated with absorbing boundary conditions when the structure of interest resides in an unbounded medium. Local boundary conditions have to be imposed on a convex outer boundary, thereby often inflating the problem size. This drawback is alleviated if the grid is truncated using exact boundary conditions that rely on a retarded-time boundary integral (RTBI) [L. Ting and M. J. Miksis, J. Acoust. Soc. Am. 80, 1825–1827 (1986)]. Unfortunately, for a 3-D computational domain comprising of O(N3) FDTD cells, where N denotes the number of cells per unit length, the evaluation of the RTBI using classical methods requires O(N4) operations per time step, which renders the RTBI approach impractical. In this presentation, it will be shown that this computational bottleneck can be alleviated by employing the plane wave time domain algorithm [A. A. Ergin et al., J. Comput. Phys. 146, 157–180 (1998)] using which the RTBI can be evaluated in O(N2<th>log2<th>N) operations. Numerical results that demonstrate the efficacy and reduced complexity of the method will be presented.

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.

Analysis of cylindrical transmission lines with the finite-difference time-domain method

In this paper, the finite-difference time-domain (FDTD) method is used to calculate the propagation characteristics of cylindrical transmission lines. An efficient two-dimensional FDTD algorithm is developed by projecting the three-dimensional FDTD cell in the cylindrical coordinates onto the r-/spl phi/ plane. An effective absorbing boundary condition is employed to truncate the mesh at its outer radial boundary. Numerical results are derived for different cylindrical transmission lines and compared to data available in the literature. Specifically, the newly proposed cylindrical coplanar waveguide is studied both theoretically and experimentally.

Comparison of the transmission-line matrix and finite-difference time-domain methods for a problem containing a sharp metallic edge

We compare Yee's finite-difference time-domain (FDTD) and symmetric condensed node transmission-line matrix (SCN-TLM) solutions for a cavity containing a metallic fin. Differential equation-based numerical methods are known to produce inaccurate results for this type of problem due to the rapid spatial variation of the field distribution in the vicinity of the singularity at the edge of the metal fin. This problem is relevant to the analysis of structures of practical interest such as microstrip and coplanar waveguides. Based on simulations, it is determined that for identical discretizations, SCN-TLM is more accurate than FDTD for this problem. We interpret this result as an indication that the symmetric condensed representation of fields (used within the SCN-TLM) lends itself to a more accurate algorithm than the distributed representation used by Yee. We estimate that the FDTD method requires 3.33 times more cells for a given three-dimensional problem than the transmission-line matrix (TLM) method (1.49 times more cells per linear dimension of the problem) in order to achieve the same accuracy. If we consider the requirements to update and store a single TLM or FDTD cell, we find the SCN-TLM algorithm is more efficient than the Yee FDTD algorithm in terms of both computational effort and memory requirements. Our conclusions regarding computational effort and memory requirements are limited to problems with homogeneous material properties.

The use of a subgrid-scale quasi-stationary approximation in finite-difference time-domain simulations to calculate the absorption by Helmholtz resonators

To calculate Helmholtz resonators using a finite-difference time-domain (FDTD) simulation technique, one has to deal with two important difficulties. First, the determining structures of a Helmholtz resonator are typically subwavelength geometries with dimensions that are smaller than the FDTD cell size normally used for the wavelengths of interest. Therefore, the FDTD cell size should be reduced, resulting in a very high computational cost. On the other hand, the viscous absorption in the resonator neck influences the resonator behavior a lot and has to be included in the calculation. The first problem was solved by using a coarse FDTD grid but applying detailed simulated quasistationary pressure distribution to modify the FDTD equations in the neighborhood of the resonator neck. For the second problem the analytical solution for viscous boundary layer absorption was introduced into the FDTD equations. However, this solution is only correct for the viscous absorption near an infinite plate. Therefore, the calculated quasi-stationary solutions were applied to correct for the nonuniform velocity distribution in the resonator neck. The results are compared with both analytical solutions and with experimental results.

Numerical studies on resonant and enhancement effects for coupling of microwave pulses into narrow slots

In this paper, modifications to the finite-difference time-domain(FD-TD) method for modeling microwave pulse coupling into a slot, which is much narrower than one conventional FD-TD cell, are discussed. The coupling process of microwave pulse into a slot is studied by using the modified FD-TD method, and the dependence of microwave coupling on slot sizes, the carrier frequencies and the polarization directions of the incident waves is analysed. Resonant and enhancement effects which occur in this process are observed. The condition at which the resonant effect takes place is also presented.

Development of a multigrid FDTD code for three-dimensional applications

Numerical modeling of realistic engineering problems using the finite-difference time-domain (FDTD) technique often requires more detail than is possible when using a uniform-grid FDTD code. We describe the development of a three-dimensional (3-D) multigrid FDTD code that focuses a large number of cells of small dimensions in the region of interest. The detailed solution procedure is described and some test geometries are solved using both a uniform-grid and the developed multigrid FDTD code to validate the results and check the accuracy of the solution. Results from these comparisons as well as comparisons between the new FDTD code and another available multigrid code are presented. In addition, results from the simulation of realistic microwave-sintering experiments in large multimode microwave cavities are given to illustrate the application of the developed method in modeling electrically large geometries. The obtained results show improved resolution in critical sites inside the 3-D multimode sintering cavity while keeping the required computational resources manageable. It is shown that it is possible to simulate the sintering of ceramic samples of 0.318-cm wall thickness in a cylindrical multimode microwave cavity with a diameter of 74 cm and a length of 112 cm using 2.24/spl times/10/sup 6/ total FDTD cells. For comparison, a total of 102/spl times/10/sup 6/ cells would have been required if a uniform-grid code with the same resolution had been used.

Hybrid FDTD large-signal modeling of three-terminal active devices

A general algorithm for including large-signal active three-terminal models into the finite-difference time-domain (FDTD) method is presented. A dynamic interface between the active device and the FDTD lattice is used to simulate the prominent nonlinear time-dependant behavior of the three-terminal active device, which is connected across multiple FDTD cells. A technique for introducing an internal electromagnetic (EM) field absorber into the FDTD three-terminal active device model in order to eliminate undesired current coupling is discussed. Numerical comparison shows this method is accurate and expected to have general utility for other complicated hybrid lumped-circuit FDTD modeling situations.

A hybrid full-wave analysis of via-hole grounds using finite-difference and finite-element time-domain methods

A hybrid full-wave analysis using finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods is developed to analyze locally arbitrarily shaped microwave structures. This hybrid method employs the standard FDTD method with super-absorbing Mur's first-order absorbing-boundary condition (ABC) and the FETD method using the second-order vector prism elements. An interpolation scheme is proposed for communicating between the FDTD and FETD fields, which will not require the effort of fitting the FETD mesh to the FDTD cells in the interface region. This method is applied to calculate the scattering parameters of single and multiple cylindrical via holes in a microstrip structure. Applying FETD to the via-hole grounds and FDTD to the remaining region preserves the advantages of both FETD flexibility and FDTD efficiency. A comparison of the results with the mode-matching data and the FDTD staircasing data verifies the accuracy of the proposed method.

A stable algorithm for modeling lumped circuit source across multiple FDTD cells

Incorporating lumped-circuit elements into finite-difference time-domain (FDTD) simulation greatly enhances the FDTD method's capability to model both distributed structures and lumped circuitries. The multiple-cell formulation proposed by C.H. Durney et al. (see ibid., vol. 6, p. 85-7, Feb. 1996) is only numerically stable for modeling structures with large permittivity. A stable algorithm for modeling material with both large and small permittivity is presented in this letter. Verification data is given together with detailed derivations.

A general formulation for connecting sources and passive lumped-circuit elements across multiple 3-D FDTD cells

A previous extension of the finite-difference time-domain (FDTD) method to include lumpedcircuit elements is further extended to model lumped-element circuits connected across multiple FDTD cells. This formulation is needed to model many kinds of circuits, like those with a transistor or other active device connected across a transmission line with more than one dielectric. The FDTD analysis of a shielded suspended microstrip transmission line excited by a current source in parallel with a resistance illustrates the usefulness of the formulation.

Finite difference time-domain calculation of transients in antennas with nonlinear loads

Transient currents for an antenna with a nonlinear load are calculated using finite-difference-time-domain (FDTD) methods. The FDTD electric field across the nonlinear load (which determines the voltage across the load) is calculated by solving a nonlinear equation at each time step. This allows the time step to be at the Courant limit, and is more efficient than reducing the time step size in all the FDTD cells to maintain stability in just the cell containing the nonlinear load. The stability of this approach relative to a simpler approach of approximating the diode as a variable resistor is demonstrated. As a validation of the method the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed and compared with calculated results obtained by another method. The approach given here extends the applicability of the FDTD method to problems involving radiation and scattering from antennas including nonlinear loads. >