Finite-difference Time-domain Solution Research Articles

Hardware implementation of a three-dimensional finite-difference time-domain algorithm

In order to take advantage of the significant benefits afforded by computational electromagnetic techniques, such as the finite-difference time-domain (FDTD) method, solvers capable of analyzing realistic problems in a reasonable time frame are required. Although software-based solvers are frequently used, they are often too slow to be of practical use. To speed up computations, hardware-based implementations of the FDTD method have recently been proposed. Although these designs are functionally correct, to date, they have not provided a practical and scalable solution. To this end, we have developed an architecture that not only overcomes the limitations of previous accelerators, but also represents the first three-dimensional FDTD accelerator implemented in physical hardware. We present a high-level view of the system architecture and describe the basic functionality of each module involved in the computational flow. We then present our implementation results and compare them with current PC-based FDTD solutions. These results indicate that hardware solutions will, in the near future, surpass existing PC throughputs, and will ultimately rival the performance of PC clusters.

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium.

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].

Extraction of equivalent‐circuit parameters of interconnection lines with the use of the finite‐difference time‐domain method

AbstractThis Letter presents a simple technique for extracting the equivalent parameters of transmission‐line interconnects based on the finite‐difference–time‐domain (FDTD) method. The transmission line containing the discontinuity is divided into a set of uniform segments of short‐length line. Next, the parameters of each of these segments are extracted by substituting the FDTD solution into the telegrapher's equations. The accuracy of the method is comparing by the results with those derived via the method of moments (MoM). The equivalent circuit can be used in a SPICE simulator to predict the performance of interconnect with a view to enhancing the characterization and design of high‐speed digital circuits. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 59–61, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10373

Power losses in steel pipe delivering very large currents

This paper presents a finite difference time domain solution for the electromagnetic fields in ferromagnetic conducting steel pipes of the type used to deliver large currents for in situ heating of heavy oil reservoirs and for in situ environmental decontamination. A method is described whereby a single measured hysteresis loop can be used to deduce the family of hysteresis loops that governs the variable magnetic behavior throughout the pipe wall. Hysteresis and eddy current losses are calculated, and it is shown that hysteresis effects greatly alter the eddy current distribution and can more than triple the total power losses in the steel pipe when compared to the power losses that would be present if hysteresis effects are ignored and magnetic permeability is assumed constant.

Design and modeling of waveguide-coupled microring resonator

The design and the simulation of high-Q microcavity ring resonators coupled to submicron-width waveguides are investigated. Nanofabrication results and optical properties of SiO 2–TiO 2 planar waveguides are presented. Key optical design parameters are characterized using Finite-Difference Time-Domain (FDTD) solutions of the full-wave Maxwell's equations.

Power Losses in Steel Pipe Deliverring Very Large Currents

This paper presents a finite difference time domain solution for the electromagnetic fields in ferromagnetic conducting steel pipes of the type used to deliver large currents for in-situ heating of heavy oil reservoirs and for in-situ environmental decontamination. A method is described whereby a single measured hysteresis loop can be used to deduce the family of hysteresis loops that governs the variable magnetic behavior throughout the pipe wall. Hysteresis and eddy current losses are calculated, and it is shown that hysteresis effects greatly alter the eddy current distribution and can more than triple the total power losses in the steel pipe when compared to the power losses that would be present if hysteresis effects are ignored and magnetic permeability is assumed constant.

Fundamental Research on Multiresolution Time Domain Scheme and Its Applications

In this paper, we have made fundamental investigation on a generalized multiresolution time domain (MRTD) scheme on the basis of the cubic spline Battle?Lemarie scaling and high-level resolution wavelet function expansions for electromagnetic applications. Focusing on a one-dimensional electromagnetic plane wave propagation problem, we summarize generalized orthogonal and semiorthogonal relations used for deriving MRTD updating equations. In this research, we employ high-level wavelets only in the extended discontinuity subregions where electromagnetic fields vary dramatically, while utilizing a scaling function in the entire computational region. It is found that the computed data is in good agreement with the analytic results and the finite difference time domain (FDTD) solutions for all cases investigated.

Finite-difference time-domain modeling of low to moderate frequency sea-surface reverberation in the presence of a near-surface bubble layer

A finite-difference time-domain (FDTD) solution to the two-dimensional linear acoustic wave equation is utilized in numerical experiments to test the hypothesis that near-surface, bubble-induced refraction can have a significant impact on low to moderate frequency sea-surface reverberation. In order to isolate the effects of bubble-modified propagation on the scattering from the air/sea interface from other possible phenomena such as scattering from bubble clouds, the bubbly environment is assumed to be range independent. Results of the study show that both the strong wind-speed dependence and the enhanced scattering levels of the order found in the reverberation data are obtained when a wind-speed-dependent bubble layer is included in the modeling.

Radiative properties of cirrus clouds in the infrared (8– [formula omitted]) spectral region

Atmospheric radiation in the infrared (IR) 8– 13 μm spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time-domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 μm . For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 and 10,000 μm over the wavelengths ranging from 8 to 13 μm . For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 μm . To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8– 13 μm spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, the extinction and absorption efficiencies are computed for hexagonal ice crystals with sizes ranging from 1 to 10,000 μm at 12 wavelengths between 8 and 13 μm . Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Ice crystals are assumed to be hexagonal columns randomly oriented in space. The bulk scattering properties are parameterized through the use of second-order polynomial functions for the extinction efficiency and the single-scattering albedo and a power-law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 μm whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 μm . For effective sizes larger than 100 μm , the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing studies of ice clouds involving IR window bands.

Ray-based amplitude tomography for crosshole georadar data: a numerical assessment

Analyses of travel times and amplitudes of crosshole georadar data provide estimates of the electromagnetic velocity and attenuation of the probed media. Whereas inversions of travel times are well established and robust, ray-based inversions of amplitudes depend critically on the complex directive properties of the georadar antennae. We investigate the variations of radiation patterns in the presence of water-filled boreholes and/or changes of electrical material properties in the vicinity of the transmitters or receivers. To assess the implications of such complicating factors for ray-based georadar amplitude tomography, we generate crosshole georadar data for a suite of canonical models using a finite difference time domain (FDTD) solution of Maxwell's equations in cylindrical coordinates. The emitting dipole-type antenna is approximated by an infinitesimal vertical electric dipole, whereas a corresponding receiving antenna is emulated by recording the vertical component of the transmitted electric field. Inversions of the amplitudes of these synthetic data demonstrate that the presence of water-filled boreholes as well as changes in the material properties along the boreholes may cause substantial artifacts in the estimated attenuation structure. Furthermore, our results indicate that ray-based amplitude tomography of crosshole georadar data is unable to constrain absolute values of attenuation. Despite these inherent limitations, the method is surprisingly robust at detecting and constraining relative changes in attenuation. In particular, we find the method to be highly effective for locating conductivity contrasts that are not associated with corresponding changes in dielectric permittivity, and hence, cannot be located by travel time tomography alone.

Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than approximately 4%. The errors in the scattering phase function are less than approximately 5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.

Hybrid MFIE/FDTD analysis of the shielding effectiveness of a composite enclosure excited by a transient plane wave

A combined magnetic field integral equation (MFIE) and finite-difference time-domain (FDTD) procedure is developed for the efficient analysis of the transient plane wave penetration inside a metallic-composite box. Suitable boundary conditions are enforced on the composite walls of the enclosure in order to link the MFIE and the FDTD solution schemes, which are applied respectively in the outer and inner volumes of the enclosure. Comparisons with a full FDTD approach are carried out to validate the procedure, The proposed hybrid MFIE/FDTD method is more efficient than the FDTD approach alone from the computational point of view, because it requires neither the discretization of the volume surrounding the enclosure, nor the use of absorbing boundary conditions to truncate the FDTD lattice.

FDTD modeling of low-frequency sea surface reverberation in the presence of a near-surface bubble layer

There exists a well-documented discrepancy between the low to moderate frequency (150 Hz<f<1.5 kHz), low-grazing angle (<30 degrees) reverberation-derived backscattering strengths collected at sea and the predictions provided by rough surface scattering models. One of the central features of the data/model comparisons in this regime is the strong wind speed dependence exhibited in the data and the very weak wind speed dependence predicted by surface scattering models. In a previous study [Keiffer et al., J. Acoust. Soc. Am. 97, 227–234 (1995)], a heuristic model was used to explore the hypothesis that bubble-induced refraction may modify the insonification of the air/sea interface and significantly enhance the surface reverberation in this frequency range. In the present work, a finite difference time domain (FDTD) solution to the linear acoustic wave equation is exercised in numerical experiments designed to unambiguously demonstrate the significant impact that near-surface, bubble-induced refraction can have on the reverberation time series and, therefore, on the surface scattering strengths.

Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method

Techniques to improve the accuracy of the finite-difference time-domain (FDTD) solutions employing sinusoidal excitations are developed. The FDTD computational domain is considered as a sampled system and analyzed with respect to the aliasing error using the Nyquist sampling theorem. After a careful examination of how the high-frequency components in the excitation cause sinusoidal steady-state errors in the FDTD solutions, the use of smoothing windows and digital low-pass filters is suggested to reduce the error. The reduction in the error is demonstrated for various cases.

Effects of reinforced concrete structures on RF communications

The proliferation of communication systems used in and around man-made structures has resulted in a growing need to determine the reflection and transmission properties of various commonly used building materials at radio frequencies typically used in businesses and residential environments. This paper describes the calculation of reflection and transmission coefficients for reinforced concrete walls as a function of wall thicknesses and rebar lattice configuration over a frequency range of 100-6000 MHz. The transmission and reflection coefficients were calculated using a finite-difference time-domain (FDTD) solution of Maxwell's equations. The rebar structures analyzed include both a two-dimensional (2-D) trellis-like structure and a one-dimensional (1-D) structure, where the reenforcing bars are all oriented in the same direction. In general, the results show that the reinforced concrete structures severely attenuate signals with wavelengths that are much larger than the rebar lattice and that the transmitted signal has a complex structure with resonances and nulls that strongly depend upon the geometry of the reinforcing structure and the concrete wall thickness.

A coherent scattering model to determine forest backscattering in the VHF-band

A coherent scattering model to determine the forest radar backscattering at VHF frequencies (20-90 MHz) has been developed. The motivation for studying this frequency band is the recent development of the CARABAS Synthetic Aperture Radar (SAR). In order to model the scattering from branches and trunks, homogeneous dielectric cylinders placed above a semi-infinite di-electric ground have been analyzed. An analytical approach, where the theoretically exact currents induced in an infinite cylinder are truncated, has been compared to a numerical solution using the finite difference time domain (FDTD) method. If the first-order coherent ray tracing is included in the analytical approach, the results match well with the numerically exact FDTD solution. The results show that, in order to determine the VHF-backscattering from a forest stand, the coherent ground interaction is an important part and has to be considered. In this paper, modeling results are in good agreement with CARABAS measurements.

Modeling electromagnetic propagation in the Earth-ionosphere waveguide

The ionosphere plays a role in radio propagation that varies strongly with frequency. At extremely low frequency (ELF: 3-3000 Hz) and very low frequency (VLF: 3-30 kHz), the ground and the ionosphere are good electrical conductors and form a spherical Earth-ionosphere waveguide. Many giants of the electromagnetics (EMs) community studied ELF-VLF propagation in the Earth-ionosphere waveguide, a topic which was critically important for long-range communication and navigation systems. James R. Wait was undoubtedly the most prolific publisher in this field, starting in the 1950s and continuing well into the 1990s. Although it is an old problem, there are new scientific and practical applications that rely on accurate modeling of ELF-VLF propagation, including ionospheric remote sensing, lightning remote sensing, global climate monitoring, and even earthquake precursor detection. The theory of ELF-VLP propagation in the Earth-ionosphere waveguide is mature, but there remain many ways of actually performing propagation calculations. Most techniques are based on waveguide mode theory with either numerical or approximate analytical formulations, but direct finite-difference time-domain (FDTD) modeling is now also feasible. Furthermore, in either mode theory or FDTD, the ionospheric upper boundary can be treated with varying degrees of approximation. While these approximations are understood in a qualitative sense, it is difficult to assess in advance their applicability to a given propagation problem. With a series of mode theory and FDTD simulations of propagation from lightning radiation in the Earth-ionosphere waveguide, we investigate the accuracy of these approximations. We also show that fields from post-discharge ionospheric currents and from evanescent modes become important at lower ELF (/spl lsim/500 Hz) over short distances (/spl lsim/500 km). These fields are not easily modeled with mode theory, but are inherent in the FDTD formulation of the problem. In this way, the FDTD solution bridges the gap between analytical solutions for fields close to and far from the source.

The far field of a borehole radar and its reflection at a planar interface

The far held of an electric Hertzian dipole located in a borehole is expressed as the product of a transmission coefficient and the far field of a dipole in a homogeneous region. The derivation uses the method of steepest descent, and gives physical insight into the wave phenomena that are important for borehole radar. The received field inside the borehole due to a planar interface located in the vicinity of the borehole is calculated using geometrical optics and the principle of reciprocity. The resulting expression is validated by numerically comparing it with a finite-difference time-domain solution. In an idealized situation, the reflection from the oil-mater boundary in a horizontal well can be detected with a borehole radar.

Self-consistent microwave field and plasma discharge simulations for a moderate pressure hydrogen discharge reactor

A self-consistent two-dimensional model of the electromagnetic field and the plasma in a hydrogen discharge system has been developed and tested in comparison to experimental measurements. The reactor studied is a 25 cm diameter resonant cavity structure operating at 2.45 GHz with a silica belljar of 10 cm diameter and 17 cm height contained within the microwave cavity. The inside of the belljar where the discharge occurs contains a substrate holder of 5 cm diameter that is used to hold substrates for diamond deposition. The electromagnetic field model solves for the microwave fields using a finite difference time-domain solution of Maxwell’s equations. The plasma model is a three energy mode (gas, molecular vibration, and electron) and nine species (H2, H, H(n=2), H(n=3), H+, H2+, H3+, H−, electron) model which accounts for non-Boltzmann electron distribution function and has 35 reactions. Simulated characteristics of the reactor in two dimensions include gas temperature, electron temperature, electron density, atomic hydrogen molar fraction, microwave power absorption, and microwave fields. Comparisons of the model are made with close agreement to several experimental measurements including coherent anti-Stokes Raman Spectroscopy measurement of H2 temperature versus position above the substrate, Doppler broadening optical emission spectroscopy (OES) measurements of H temperature versus pressure, actinometry measurements of the relative H atom concentration, Hα OES intensity measurements versus position, and microwave electric field measurements. The parameter range studied includes pressures of 2500–11 000 Pa, microwave powers of 300–2000 W, and three vertical positions of the substrate holder.

Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition

A three-dimensional finite-difference time-domain (FDTD) program has been developed to provide a numerical solution for light scattering by nonspherical dielectric particles. The perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computational domain. As a result of using the PML ABC, the present FDTD program requires much less computer memory and CPU time than those that use traditional truncation techniques. For spheres with particle-size parameters as large as 40, the extinction and absorption efficiencies from the present FDTD program match the Mie results closely, with differences of less than approximately 1%. The difference in the scattering phase function is typically smaller than approximately 5%. The FDTD program has also been checked by use of the exact solution for light scattering by a pair of spheres in contact. Finally, applications of the PML FDTD to hexagonal particles and to spheres aggregated into tetrahedral structures are presented.