Conformal Finite-difference Time-domain Method Research Articles

Wideband performance limitations of the C-FDTD in the discretization impoverishment of a curved surface

PurposeThis paper aims to explore the limitations of the conformal finite difference time-domain method (C-FDTD or Dey–Mittra) when modeling perfect electric conducting (PEC) and lossless dielectric curved surfaces in coarse meshes. The C-FDTD is a widely known approach to reduce error of curved surfaces in the FDTD method. However, its performance limitations are not broadly described in the literature, which are explored as a novelty in this paper.Design/methodology/approachThis paper explores the C-FDTD method applied on field scattering simulations of two curved surfaces, a dielectric and a PEC sphere, through the frequency range from 0.8 to 10 GHz. For each sphere, the mesh was progressively impoverished to evaluate the accuracy drop and performance limitations of the C-FDTD with the mesh impoverishment, along with the wideband frequency range described.FindingsThis paper shows and quantifies the C-FDTD method’s accuracy drops as the mesh is impoverished, reducing C-FDTD’s performance. It is also shown how the performance drops differently according to the frequency of interest.Practical implicationsWith this study, coarse meshes, with smaller execution time and reduced memory usage, can be further explored reliably accounting the desired accuracy, enabling a better trade-off between accuracy and computational effort.Originality/valueThis paper quantifies the limitations of the C-FDTD in coarse meshes in a wideband manner, which brings a broader and newer insight upon C-FDTD’s limitations in coarse meshes or relatively small objects in electromagnetic simulation.

Analysis of GPR Wave Propagation in Complex Underground Structures Using CUDA-Implemented Conformal FDTD Method

Ground penetrating radar (GPR), as a kind of fast, effective, and nondestructive tool, has been widely applied to nondestructive testing of road quality. The finite-difference time-domain method (FDTD) is the common numerical method studying the GPR wave propagation law in layered structure. However, the numerical accuracy and computational efficiency are not high because of the Courant-Friedrichs-Lewy (CFL) stability condition. In order to improve the accuracy and efficiency of FDTD simulation model, a parallel conformal FDTD algorithm based on graphics processor unit (GPU) acceleration technology and surface conformal technique was developed. The numerical simulation results showed that CUDA-implemented conformal FDTD method could greatly reduce computational time and the pseudo-waves generated by the ladder approximation. And the efficiency and accuracy of the proposed method are higher than the traditional FDTD method in simulating GPR wave propagation in two-dimensional (2D) complex underground structures.

A Conformal FDTD Method With Accurate Waveport Excitation and S-Parameter Extraction

We demonstrate a conformal finite-difference time domain (CFDTD) technique with accurate waveport excitation and S-parameter extraction. We discuss, under the CFDTD framework, object modeling with effective subcell material, impedance calibration for the conformal modeled coaxial feed, waveport mode calculation with a newly developed conformal 2-D finite-difference frequency domain solver, waveport excitation with a modified total field scattered field method, and a modified S-parameter extraction scheme that is compatible with the CFDTD method. Lastly, we present two specific validation cases intended as relevant precursors to the inverse scattering application: modeling of the reflection coefficient of a tapered patch antenna and modeling of the transmission coefficient in a probe-fed rectangular waveguide.

誘電性散乱体粒子の接近がインライン・ホログラフィに及ぼす影響のConformal FDTD(2,4)法による検討

In order to numerically simulate the formation of hologram appearing in the in-line holography method with high precision, improvement for FDTD (2,4) method was proposed. Examination about the effect of improvement showed that proposed improvement remarkably suppress the phase error of electro-magnetic wave to negligible level even in the case where large-scale calculation domain is ordered to treat multiple scattering problems, while the ordinal FDTD (2,4) method causes serious error in such cases. In addition, Conformal FDTD methods is combined with the above-mentioned FDTD (2,4) method with improvement in order to suppress the error associated with step-wise approximation of particle shape. At the next stage, examinations were carried out using the above-mentioned Conformal FDTD (2,4) method, about the influence of closeness between two particles on the location error of reconstructed image in the in-line holography method. Results of numerical simulation showed that reconstructed images of particles are deformed when the distance between two particles is shortened, and error appears in the evaluation of particle location. Location error is decreased with elongation of distance between two particles when they go away in the perpendicular direction to incident beam. On the other hand, contrary tendency partly appears when two particles go away in the parallel direction with incident beam. Additionally, it was considered that difference of plane of polarization.

A Hybrid Implicit–Explicit and Conformal (HIE/C) FDTD Method for Efficient Electromagnetic Simulation of Nonorthogonally Aligned Thin Structures

In a conventional finite-difference time-domain (FDTD) method, the computational cost increases as a grid spacing decreases because the number of unknowns increases and a time step size decreases to fulfill a numerical stability condition. Especially, it is inherently time-consuming to analyze thin structures such as a printed circuit board (PCB) and nonorthogonally aligned objects such as interconnection patterns on the PCB. In this paper, we propose an efficient electromagnetic simulation technique which is constructed by combining a hybrid implicit–explicit (HIE)-FDTD method and a conformal FDTD (CFDTD) method. The proposed technique can avoid the aforementioned problems by exploiting advantages of the HIE-FDTD and CFDTD methods. An example model of the interconnection pattern on the PCB is analyzed by the proposed and conventional methods, and we compare their accuracy and efficiency.

The Conformal HIE-FDTD Method for Simulating Tunable Graphene-Based Couplers for THz Applications

An improved hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is proposed for simulating graphene-based patch couplers at terahertz (THz) for different physical and geometrical parameters, where the Drude model of monolayer graphene and the associated auxiliary differential equation (ADE) technique are implemented. In order to accurately model the curved graphene boundaries, the conformal FDTD method is further hybridized with the HIE-FDTD method, which results in a conformal HIE-FDTD method. Numerical results are presented for S-parameters and field distributions of the coupler, which can be adjusted effectively by changing the chemical potential and layer number of graphene patch or substrate permittivity.

G1000704 散乱体粒子の接近がインライン・ホログラフィに及ぼす影響のConformal FDTD(2,4)法による検討

In order to numerically simulate the formation of hologram appearing in the in-line holography method with high precision, improvement for FDTD (2,4) method was proposed. Examination about the effect of improvement showed that proposed improvement remarkably suppress the phase error of electro-magnetic wave to negligible level even in the case where large-scale calculation domain is ordered to treat multiple scattering problems, while the ordinal FDTD (2,4) method causes serious error in such cases. In addition, Dey-Mittra method, which is one of the conformal FDTD methods, is combined with the above-mentioned FDTD (2,4) method with improvement in order to suppress the error associated with step-wise approximation of particle shape. At the next stage, examinations were carried out using the above-mentioned conformal FDTD (2,4) method, about the influence of closeness between two particles on the location error of reconstructed image in the in-line holography method. Results of numerical simulation showed that reconstructed images of particles are deformed when the distance between two particles is shortened, and error appears in the evaluation of particle location- Location error is decreased with elongation of distance between two particles when they go away in the perpendicular direction to incident beam. On the other hand, contrary tendency partly appears when two particles go away in the parallel direction with incident beam.

A new parallel meshing technique integrated into the conformal FDTD method for solving complex electromagnetic problems

A new efficient parallel finite-difference time-domain (FDTD) meshing algorithm, based on the ray tracing technique, is proposed in this paper. This algorithm can be applied to construct various FDTD meshes, such as regular and conformal ones. The Microsoft F# language is used for the algorithm coding, where all variables are unchangeable with its parallelization advantage being fully exploited. An improved conformal FDTD algorithm, also integrated with an improved surface current algorithm, is presented to simulate some complex 3D models, such as a sphere ball made of eight different materials, a tank, a J-10 aircraft, and an aircraft carrier with 20 aircrafts. Both efficiency and capability of the developed parallel FDTD algorithm are validated. The algorithm is applied to characterize the induced surface current distribution on an aircraft or a warship.

Accurately and Efficiently Studying the RF Structures Using a Conformal Finite-Difference Time-Domain Particle-in-Cell Method

This work introduces a conformal finite difference time domain (CFDTD) particle-in-cell (PIC) method to accurately and efficiently study electromagnetic or radio frequency (RF) structures and their interactions with charged particles. For illustration, the dispersion relation of an A6 relativistic magnetron has been determined and a preliminary hot test including electrons has been done. The accuracy of the CFDTD method is measured by comparing with calculations based on the finite element method. The results show that an accuracy of 99.4% can be achieved by using only 10,000 mesh points with the Dey-Mittra algorithm as implemented in the CFDTD method. By comparison, a mesh number of 250,000 is needed to preserve 99% accuracy using a staircased FDTD method. This suggests one can more efficiently and accurately study the hot tests of microwave tubes or the interactions of charged particles and RF structures using the CFDTD PIC method than a conventional FDTD one.

Optimized Conformal FDTD (2, 4) Method for Calculating Reflected and Diffracted Electromagnetic Fields of Perfectly Conducting Wedges

An optimized conformal finite-difference time-domain (FDTD) (2, 4) method is proposed for calculating reflected, diffracted, and total fields of two- and three-dimensional (2- and 3-D) perfectly conducting (PEC) wedges with an electromagnetic pulse (EMP) incidence, where one low-cost coefficient-modification (CM) technique is implemented for effectively reducing its numerical dispersion error. For the 2-D geometries, both reflected and diffracted fields are extracted from the whole calculation domain of FDTD (2, 4), and excellent agreement is achieved between the calculated diffraction coefficient and the analytical one obtained by high frequency approximation method of UTD. While for the 3-D wedges, even with the coarse FDTD cells adopted, such an optimized method still possesses the capability for getting more accurate diffracted fields in comparison with the conventional FDTD.

A DISPERSIVE CONFORMAL FDTD TECHNIQUE FOR ACCURATE MODELING ELECTROMAGNETIC SCATTERING OF THZ WAVES BY INHOMOGENEOUS PLASMA CYLINDER ARRAY

A dispersive conformal FDTD method has been proposed to accurately model the interface between two adjacent dispersive mediums and implemented to study the scattering of THz electromag- netic (EM) waves by inhomogeneous collisional plasma cylinder array. The method is based on the technology of area average, which is dif- ferent from existing dispersive conformal FDTD schemes. Numerical results show that the proposed method enhances the accuracy level compared to the staircasing FDTD scheme involved in the inhomoge- neous plasma. It is interesting to flnd that the THz EM waves can propagate through the plasma array more easily with higher frequen- cies or larger separations, hence the scattering width in the backward direction becomes smaller, and the forward scattering exhibits a little difierent. This study will be useful for further designing intelligent plasma antenna arrays in the THz band and terahertz reentry teleme- try through plasma.

New Development of Parallel Conformal FDTD Method in Computational Electromagnetics Engineering

In this paper, we summrize the new development of hardware-acceleration techniques and a parallel conformal Finite-Difference Time-Domain (FDTD) method in computational electromagnetics engineering. We investigate the performance of a parallel conformal FDTD method on different hardware platforms, such as Intel and AMD processors, with vector-arithmetic logic unit (VALU) acceleration, a regular PC cluster, a high-performance server cluster, the use of a graphics-processing unit (GPU), and an IBM CELL processor. The FDTD method, which is parallel in nature, is one of the best candidate numerical methods for using multiple-core processors and computer clusters to efficiently simulate various electromagnetic problems. Several representative examples, such as a UWB (ultra-wideband) antenna array and reflector antennas, are employed to demonstrate the engineering applications of the parallel conformal FDTD method.

A 3-D Analysis of a Microfabricated Ladder Slow-Wave Structure for a Millimeter-Wave Traveling-Wave Tube

The design and the analysis of a ladder slow-wave structure (SWS) operating at 50 GHz is presented. A 3-D particle-in-cell (PIC) modeling of a ladder SWS is presented for the first time. Compared with a conventional helix circuit, the ladder SWS provides wide bandwidth, high interaction impedance, and ease of manufacturing at millimeter wavelengths. A small-signal code based on Pierce's theory was developed to determine the dimensions and the small-signal characteristics of the device. Cold- and hot-test simulations were performed using High Frequency Structure Simulator and VORPAL codes. VORPAL, a 3-D PIC simulator that makes use of the conformal finite-difference time-domain method, predicts a small-signal gain of 15 dB and an instantaneous bandwidth of 6% for a 68-period ladder SWS that is driven by a 22-kV and 196-mA electron beam. Dispersion characteristics, large-signal characteristics, and nonlinear-beam dynamics are investigated.

High-Performance Conformal FDTD Techniques

In this article we have presented the major features of the parallel conformal FDTD method and its applications to the electromagnetic simulation of microwave devices and components. We have used the parallel conformal FDTD code and have run it on parallel platforms to simulate a number of representative problems that find important engineering applications. We verified the performance of the parallel FDTD code when applied to these problems and demonstrated that the parallel conformal FDTD code not only exhibits excellent parallel efficiency, but also provides savings in computer memory usage when compared to other codes that are based on similar algorithms. The combination of these two features enables the parallel conformal FDTD code to simulate large, complex and practical problem geometries in a time-efficient manner.

A New Scheme for the Conformal FDTD Method to Calculate the Radar Cross Section of Perfect Conducting Curved Objects

The chief shortcoming of the conformal finite-difference time-domain (CFDTD) method is the global time-step reduction in order to avoid instability arising from small irregular cells. In this letter, we introduce a new conformal scheme to overcome this problem for the CFDTD method. The time-step reduction is applied only locally to the small irregular cells, which is only 1/3 of that in the regular cells. In order to update the electric field at the interface between the small irregular cell and its adjacent cells, extra magnetic fields next to the small irregular cell are introduced. Through this scheme, the time-step reduction is limited to a few small cells, and the numerical simulation can be the most efficiently implemented in the FDTD framework. Numerical accuracy is verified by comparison with the conventional CFDTD method for the radar cross section (RCS) of perfect conducting curved objects.

Complete analysis of photonic crystal fibers by full-vectorial 2D-FDTD method

In this paper, an extended finite difference time domain (FDTD) algorithm for the full-vectorial analysis of photonic crystal fibers has been derived. For achieving a good convergence and high accuracy, a kind of modified conformal FDTD method has been applied. An anisotropic perfectly matched layer for truncation of boundary conditions has been introduced. Material and chromatic dispersions are numerically investigated for the photonic crystal fibers with different dimensions and geometrical parameters and different dispersion behaviors are exhibited.

Simulation model for moving food packages in microwave heating processes using conformal FDTD method

A numeric model was developed to couple electromagnetic (EM) and thermal field calculations in packaged foods moving in pressurized 915 MHz microwave (MW) cavities with circulating water at above 120 °C. This model employed a commercial EM package with a customized heat transfer sub-model to solve EM field and thermal field equations. Both methods applied finite-difference time-domain (FDTD) method. An interface was built to facilitate the communication between electromagnetic and thermal models to incorporate the coupling feature which is unique to microwave heating process. Special numerical strategies were implemented to simulate the movement of food packages. The simulation model was validated with a pilot-scale microwave system using direct temperature measurement data and indirect color patterns in whey protein gels via formation of the thermally induced chemical marker M-2. Good agreements were observed. Four cases were studied to investigate the influence of power input and package gaps on heating uniformity. These applications demonstrated the flexibility of the model to allow its usage for system and process optimization.

A 3-D Enlarged Cell Technique (ECT) for the Conformal FDTD Method

In this paper, we present an enlarged cell technique (ECT) to avoid the time step reduction encountered in the conformal finite-difference time-domain (CFDTD) method due to small irregular cells truncated by metallic boundaries. We focus our efforts on the discussion of the accuracy and stability of the ECT and its comparison with other conformal methods, especially the one called the uniformly stable conformal (USC) method. We also provide a simplified ECT, which is much easier to implement. In the ECT, a stability criterion is first constructed to identify instable irregular cells, i.e., those having so small an area to cause instability. Those instable cells are then enlarged into their adjacent cells to obtain a large, stable area. Careful treatment is performed on the communication between the intruding and intruded cells in terms of electromotive force by keeping the total electromotive force conservative. This technique is verified by several 3-D numerical experiments. Results show that the ECT is second-order accurate and numerically stable at the regular Courant time step limit.

An Attempt to Improve the Dey–Mittra Formalism and Its Application in Numerical Modeling of Continuous Long Slot Leaky-Wave Antenna

A detailed analysis of the continuous long slot leaky-wave antenna working in millimeter-waveband is carried out by the piecewise integration conformal finite-difference time-domain (CFDTD) method. Firstly, the piecewise integration CFDTD method is presented. Secondly, the key steps involved in the design scheme are summarized. Then a continuous long slot leaky-wave antenna in Ka band is designed and fabricated as an example. Moreover, the return loss of the E-plane Tee-junction (ET) and the radiation pattern of the leaky-wave antenna are simulated by the piecewise integration CFDTD method. Finally, the results are compared with those of the staircase FDTD method and experimental data.

A New Method to Avoid Reduction of Time Step in the CP-FDTD Method

A new CP-WCS FDTD method is developed to avoid the time step reduction in the conformal path FDTD method. The stability condition in this method is not related with the shape and size of the distorted cell, and the time step size in this method is only determined by the space discretization perpendicular to the curved metal surface. The CP-WCS FDTD method has the same accuracy as that for the CP FDTD method, and due to large time step size can be used, the CP-WCS FDTD has higher computation efficiency, which is demonstrated by numerical examples.