Traditional Finite-difference Time-domain Method Research Articles

A parallel finite-element time-domain method for transient electromagnetic simulation

The finite-difference time-domain (FDTD) method has been widely used to perform transient electromagnetic simulation. Compared to the traditional FDTD method, the finite-element time-domain (FETD) method with unstructured meshes and an adaptive time-stepping scheme has the potential to dramatically cut down the number of unknowns and the number of time steps. However, with a need to solve a large-scale unstructured sparse matrix at every time step, the FETD method is generally difficult to scale with the available parallel computing resources. To make efficient use of the multicore resources in current computing platforms, we designed a parallel FETD method that used multiple threads to accelerate the key steps for solving a large sparse matrix, including the construction of the preconditioner and matrix-vector multiplication. Using a customized incomplete Cholesky preconditioner, we achieved faster convergence than many existing preconditioners and a scalable parallel performance over multiple cores. To further reduce the total calculation time, we implemented an overlapping scheme and a preconditioner-reusing scheme. The overlapping scheme executed the solver computation and the preconditioner computation concurrently using different parts of the parallel resources. The preconditioner reusing scheme reduced the need to recompute preconditioners when increasing the time-step size, thus reducing the frequency of the less scalable preconditioner computations. It brought performance benefits by reducing the frequency of less scalable preconditioner computation. Computed parallel FETD results showed the same level of accuracy as FDTD results. In terms of parallel performance, using eight cores, the method cut execution time by a factor of 4 (i.e., 50 parallel efficiency). For a realistic salt model, we simulated TEM responses from 0.01 s to 30 s in 5 min, using hundreds of CPU cores.

Wavelet-Based FDTD and Tunable High Resolution Estimator for Calculation of Band Structures in Two-Dimensional Phononic Crystals

This paper discusses the wavelet-based Finite Difference Time Domain (FDTD) method and a tunable high resolution estimator with a specific problem of sound wave propagation through phononic crystals. If the band structures of a phononic crystal are calculated by the traditional FDTD method combined with the fast Fourier transform (FFT), some disadvantages, such as time consuming and the numerical instability of FDTD iterations are encountered. Moreover, good frequency estimation can only be ensured by the postprocessing of sufficiently long time series. In this paper, a wavelet-based FDTD and a tunable high resolution estimator based on a bank of filters are proposed to overcome these difficulties. Numerical results for twodimensional phononic crystal show that the wavelet-based FDTD method improves the efficiency of the time stepping algorithm and the stability of iterations, and tunable high resolution estimator shows the advantages over the FFT-based spectral estimation.

Parallel Numerical Simulations of Three-Dimensional Electromagnetic Radiation with MPI-CUDA Paradigms

Using parallel computation can enhance the performance of numerical simulation of electromagnetic radiation and get great runtime reduction. We simulate the electromagnetic radiation calculation based on the multicore CPU and GPU Parallel Architecture Clusters by using MPI-OpenMP and MPI-CUDA hybrid parallel algorithm. This is an effective solution comparing to the traditional finite-difference time-domain method which has a shortage in the calculation of the electromagnetic radiation on the problem of inadequate large data space and time. What is more, we use regional segmentation, subregional data communications, consolidation, and other methods to improve procedures nested parallelism and finally verify the correctness of the calculation results. Studying these two hybrid models of parallel algorithms run on the high-performance cluster computer, we draw the conclusion that both models are suitable for large-scale numerical calculations, and MPI-CUDA hybrid model can achieve higher speedup.

A New Unconditionally Stable Scheme for FDTD Method Using Associated Hermite Orthogonal Functions

An unconditionally stable solution using associated Hermite (AH) functions is proposed for the finite-difference time-domain (FDTD) method. The electromagnetic fields and their time derivatives in time-domain Maxwell's equations are expanded by these orthonormal basis functions. By applying Galerkin temporal testing procedure to these expanded equations the time variable can be eliminated from the calculations. A set of implicit equations is derived to calculate the magnetic filed expansion coefficients of all orders of AH functions for the temporal variable. And the electrical field coefficients can be obtained respectively. With the appropriate translation and scale parameters, we can find a minimum-order basis functions subspace to approach a particular electromagnetic field. The numerical results have shown that the proposed method can reduce the CPU time to 0.59% of the traditional FDTD method while maintaining good accuracy.

A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

This paper presents a novel 3-D leapfrog hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman–Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by $e$ and $h$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant–Friedrichs–Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.

Wavelet-Based FDTD and High Resolution Spectral Estimation for Calculation of Band Structures in Two-Dimensional Phononic Crystals

This paper discusses the wavelet-based Finite Difference Time Domain (FDTD) method and high resolution spectral estimation with a specific problem of sound wave propagation through phononic crystals. If the band structures of a phononic crystal are calculated by the traditional FDTD method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome the difficulty. Numerical simulation results for two-dimensional phononic crystal show that, the wavelet-based FDTD method improves the efficiency of the time stepping algorithm, and high resolution spectral estimation shows the advantages over the classic FFT-based postprocessing.

A New Method to Analyze Broadband Antenna-Radome Interactions in Time-Domain

Based on the new time-domain finite integration theorem (TDFIT), a fast and accurate method is proposed to analyze broadband antenna-radome interactions in time domain. Due to the time-domain feature, broadband characteristic is obtained in a single simulation. In numerical simulations, the antenna array is placed inside an enclosed or semi-closed radome by using a presented local waveguide port. The staircase error in traditional finite-difference time-domain method is reduced by a novel conformal technique. An illustrating broadband antenna array with radome, operating at millimeter wave frequency is analyzed and optimized to show the high performance of our method. A new broadband transmittance of the antenna-radome system is proposed to incorporate the side lobe effect, and it is treated as the objective function to optimize the parameters of the antenna-radome system. Furthermore, the full wave simulation, combined with an artificial neural network (ANN) algorithm, is utilized to accelerate the antenna-radome optimization. About half of the time for computation has been reduced.

Applications of the multidomain pseudospectral time-domain algorithm for waveguide structures

The authors have analysed the complex waveguide structures by the multidomain pseudospectral time-domain (MPSTD) algorithm, and discussed the design of a filtering procedure through improving the stability of the MPSTD method for the corner singularities. These numerical results of the MPSTD method have shown an excellent agreement with those results of the analytical solution and the traditional finite-difference time-domain method for the resonant frequencies of the waveguide structures. It is evident that the MPSTD method can achieve high efficiency and accuracy when we use to analyse inhomogeneous media and curved objects.

WAVEGUIDE SIMULATION USING THE HIGH-ORDER SYMPLECTIC FINITE-DIFFERENCE TIME-DOMAIN SCHEME

Abstract—The high-order symplectic finite-difference time-domain scheme is applied to modeling and simulation of waveguide structures. First, the perfect electric conductor boundary is treated by the image theory. Second, to excite all possible modes, an efficient source excitation method is proposed. Third, the modified perfectly matched layer is extended to its high-order form for absorbing the evanescent waves. Finally, a high-order scattering parameter extraction technique is developed. The cases of waveguide resonator, waveguide discontinuities, and periodic waveguide structure demonstrate that the high-order symplectic finite-difference time-domain scheme can obtain better numerical results than the traditional finite-difference timedomain method and save computer resources.

Implementation of ADI-FDTD subgrids in ground penetrating radar FDTD models

Realistic numerical modeling of ground penetrating radar (GPR) using the finite-difference time-domain (FDTD) method could greatly benefit from the implementation of subgrids – supporting finer spatial resolution – into the conventional FDTD mesh. This is particularly important, when parts of the computational domain need to be modeled in detail or when there are features or regions in the overall computational mesh with values of high dielectric constant supporting propagation of waves at very short wavelengths. A scheme that simplifies the process of implementing these subgrids into the traditional FDTD method is presented. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Because ADI-FDTD is unconditionally stable its time-step can be set to any value that facilitates the accurate calculation of the fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a costly time-interpolation scheme. This paper discusses the performance of ADI-FDTD subgrids when implemented into the traditional FDTD method, using different communication schemes for the information exchange at the boundary of the two grids. The developed algorithm, can handle cases where the subgrid crosses dielectrically inhomogeneous media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented.

Underwater FDTD Simulation at Extremely Low Frequencies

This letter describes the application of the finite-difference time-domain (FDTD) method to the simulation of extremely low frequency (ELF) electromagnetic signals under water. This requires substantial modification to the traditional FDTD method, as well as the development of an analytic method needed to verify the accuracy of the FDTD method.

AN ENHANCED FDTD MODEL FOR COMPLEX LUMPED CIRCUITS

One of most difficult challenges in simulating hybrid RF systems by finite-difference time-domain (FDTD) method is to construct the models for active and lumped elements. In this article, by combining the circuit equations with an integral transform, an enhanced FDTD method is proposed to model the hybrid lumped network which consists of nonlinear and high order linear elements with arbitrary connections. Based on this model, an active radiation system is analyzed. And it shows the application extension of the traditional FDTD method.

The unconditionally stable Crank Nicolson FDTD method for three-dimensional Maxwell's equations

In this paper, an accurate and computationally implicit 3D finite-difference time-domain (FDTD) method based on the unconditionally stable Crank–Nicolson scheme (3D CN-FDTD) is presented. The source excitation in 3D CN-FDTD is described and the numerical simulation of the 3D CN-FDTD method is demonstrated through numerical examples. The results of this method, the ADI-FDTD method, and traditional FDTD schemes are compared. A good agreement is obtained for the 3D CN-FDTD method with time steps greatly more than the Courant–Friedrich–Levy (CFL) limit and the traditional Yee FDTD method. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1619–1622, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21684

Pattern reconfigurable leaky-wave antenna design by FDTD method and Floquet's Theorem

A pattern reconfigurable millimeter-wave coplanar waveguide leaky-wave antenna is designed by using the finite-difference time-domain (FDTD) method combined with Floquet's theorem and the simple linear interpolation technique. The concept of equivalent period is presented for mixed-periodic structures. The novel design process results in a reduction in the design time compared with that of the traditional FDTD method.

Modeling of magnetic loss in the finite-element time-domain method

The modeling of magnetically lossy media in the finite-element time-domain (FETD) method is substantially different from the simple treatment in the frequency-domain finite-element method. Two FETD formulations are presented and their numerical implementations are discussed. One is applicable to the case where each element is homogeneous, and the other can be applied to inhomogeneous elements. Verification is provided through comparison with results obtained from the traditional finite-difference time-domain method that solves the two Maxwell curl equations. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 165–168, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20932

Parallel implementation of the biorthogonal multiresolution time-domain method.

The three-dimensional biorthogonal multiresolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly supported wavelet functions as the basis, whereas we employ the Cohen-Daubechies-Fouveau (CDF) biorthogonal wavelets. When a CDF-wavelet expansion is used, the spatial-sampling rate can be reduced considerably compared with that of the conventional finite-difference time-domain (FDTD) method, implying that larger targets can be simulated without sacrificing accuracy. We implement the Bi-MRTD on a cluster of allocated-memory machines, using the message-passing interface (MPI), such that very large targets can be modeled. Numerical results are compared with analytical ones and with those obtained by use of the traditional FDTD method.

Analysis of Curved Boundaries by FDTD and FE Methods

Curved waveguide surfaces have been dealt with by using modified finite difference time domain (FDTD), finite element method (FEM) and hybrid methods. The propagation characteristics and S-parameters of the circular waveguides have been determined, and results compared with the analytic results, thus determining the computational efficiency of each of the method. Both FDTD and FE techniques are extensively used in the analysis and design of microwave problems. For the analysis of curved boundary, however, the traditional FDTD method suffers from significant degradation in accuracy due to staircasing approximation. A novel approach is presented here which combines the efficiency of the Cartesian mesh with the accuracy of the conformal grid. Further, an efficient finite element method is presented in which a variational expression is formulated in terms of transverse electric and magnetic field components. The method can be applied to anisotropic media also. Finally a partially prism gridded FDTD method is proposed which hybridizes the prism based FEM to handle the curved boundaries and rectangular gridded FDTD for most of the regular region.

Multiresolution analysis similar to the FDTD method-derivation and application

A three-dimensional (3-D) multiresolution analysis procedure similar to the finite-difference time-domain (FDTD) method is derived using a complete set of three-dimensional orthonormal bases of Haar scaling and wavelet functions. The expansion of the electric and the magnetic fields in these basis functions leads to the time iterative difference approximation of Maxwell's equations that is similar to the FDTD method. This technique effectively models realistic microwave passive components by virtue of its multiresolution property; the computational time is reduced approximately by half compared to the FDTD method. The proposed technique is validated by analyzing several 3-D rectangular resonators with inhomogeneous dielectric loading. It is also applied to the analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors to extract their S-parameters and field distributions. The results of the proposed technique agree well with those of the traditional FDTD method.

A new finite-difference time-domain formulation and its equivalence with the TLM symmetrical condensed node

A finite-difference time-domain (FD-TD) formulation is described. It is shown that the finite-difference time-domain formulation is equivalent to the symmetrical condensed node model used in the transmission line matrix (TLM) method. The TLM method can be formulated exactly in a finite-difference form in terms of total field quantities. It is shown that, due to a better field resolution and fulfilment of continuity conditions, the FD-TD formulation or its TLM equivalent model give better convergence and accuracy than the traditional FD-TD method. This is illustrated by numerical results pertaining to a finned waveguide.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>