Analysis of time reversed electromagnetic wave propagation with FDTD method

New version of FDTD with GFM program in Schwarzschild space–time

The finite difference time domain (FDTD) method has been proposed and used for sound field simulation. To reproduce actual sound wave propagation in sound field simulations, it is necessary to apply the radiation characteristics. With the FDTD method, radiation characteristics can be applied by setting sound pressure in a dense grid arrangement. However, conventional techniques for capturing radiation characteristics use a sparse array of microphones and are considered insufficient for the FDTD simulation. Furthermore, the technique required to apply captured acoustic signals in a dense grid arrangement with the FDTD method has not been considered. In this paper, we propose a novel hardware and software system that captures the radiation characteristics for a dense grid arrangement and applies them to the FDTD method, while controlling the sound wave propagation with the non-propagation region. The proposed system produces the average differences from measured values of sound pressure, propagation time, center frequency, and log-spectral distortion of 1.8 dB, 0.04 ms, 700 Hz, and 3.5 dB, respectively, which is more accurate than the conventional techniques. The result shows that this system is useful for improving the accuracy of sound wave propagation reproduction with the sound field simulation.

In this paper, we analyze the propagation effects on lightning‐radiated electromagnetic fields over mountainous terrain by using a three‐dimensional (3‐D) finite difference time domain (FDTD) method. We also discuss the time delay error in the time‐of‐arrival (ToA) technique currently used to locate lightning in detection networks, specifically. Furthermore, the accuracy of different approximate methods presented in the literature is discussed and tested by using our 3‐D FDTD method. It is found that (1) the time delays and amplitudes of the lightning‐radiated electromagnetic fields can be significantly affected by the presence of a mountainous terrain and associated diffraction phenomena; (2) for a finitely conducting ground, the time delay shows a slight increase with the increase of the observation distance, but the time delay resulting from the finite ground conductivity appears to be smaller than that caused by the mountainous terrain; and (3) the timing error associated with the ToA technique depends on the threshold times. Threshold times of 10% and 20% of the peak provide very similar results compared to those corresponding to the peak of the first derivative of the magnetic field, and the threshold time exceeds 50% of the initial rising amplitude of the signal. Furthermore, we have assessed the accuracy of two simplified methods (terrain‐envelope method and tight‐terrain fit method) to account for the time delays resulting from the propagation in a mountainous terrain. It is found that both methods result in time delays that are in reasonable agreement but always overestimating the results obtained using the full‐wave 3‐D FDTD approach for the perfectly conducting ground. These two methods represent interesting alternatives to account for the time delay over a nonflat terrain using the terrain model.

This paper presents an efficient hybrid method consisting of finite-difference time-domain (FDTD) method, transmission line (TL) equations, and a novel time-domain S -parameter cascade (TD-SC) technique, which can be directly applied in time domain for the EMI analysis of transmission line network (TLN) in shielded electronic device excited by ambient electromagnetic wave. The FDTD method combined with an auto mesh generator is utilized to model the shielded structure of an arbitrary electronic device rapidly, and obtain the excitation fields of the TLN exactly. Then, the TD-SC technique based on TL equations, FDTD method, and S parameter of circuits is proposed for the further EMI analysis of the TLN consisting of multistage TLs and circuits. It has the advantage of without modeling the fine structures of TLs and circuits directly. Numerous examinations exhibit that this hybrid method is an efficient method for the EMI analysis of TLN by comparing with a three-dimensional FDTD method. The computation time and memory cost by this hybrid method is much less than that of the FDTD method, because the hybrid method provides a fast way to compute the transient responses on TLN in which the TLs and circuits do not need to be meshed.

The finite difference time domain method and finite element methods have proven to be highly effective techniques for the full wave analysis of microwave circuits and resonators. The finite difference time domain (FDTD) method is highly efficient, explicit and parallelizable. Finite element methods have been used in the frequency domain and in the time domain using implicit methods. Implicit methods require a solution of a linear system of equations at each time step. For the finite element time domain (FETD) algorithm to be competitive with the FDTD, the number of time iterations required for a simulation must be significantly less. An unconditionally stable FETD algorithm is used. The variational formulation is based on the vector wave equation. Unconditional stability is achieved by using a modified Newmark-Beta time integration technique. In addition, this algorithm is implemented on parallel message passing computers using a finite element tearing and interconnecting scheme. Some numerical examples based on cavity resonator problems are presented to demonstrate the efficiency and accuracy of the method and the parallel efficiency of the algorithm.

R wave is short for Rayleigh wave. R wave,on which the effect of gravity is generally inevitable,has received considerably extensive attention and been widely used in many fields,such as geological exploration,nondestructive test,etc. The effects of gravity on R wave velocity for elastic parameters were further analyzed based on available R wave velocity function,and the applicable range of the approximate one was given as well. Wave propagation through quasi-half-space isotropic linear elastic medium with gravity,under the excitation of differentiated Gaussian pulse( DGP) was studied by finite difference time domain( FDTD) method with staggered grid discretization,and extended boundary conditions were introduced.Velocity values obtained were closer to the theoretical ones. Meanwhile,the influence of gravity on time domain,frequency domain response was discussed. By analyzing the theoretical and numerical results,it is necessary to take the effect of gravity into account in simulation for more accurate prediction.

A modified (2M, 4) scheme of the high-order two-dimensional finite-difference time-domain (FDTD) method based on wave equation is proposed. It has the fourth-order accuracy in the time domain using the symplectic integrator propagator, and the 2M-order accuracy in the space domain using the discrete singular convolution method. The distinctive features between the modified scheme and the traditional (2M, 4) FDTD based on Yee algorithm are listed as follows. First, the modified scheme is based on the wave equation. Second, the computational region is discretized by uniform mesh rather than the Yee mesh. Third, the modified scheme costs less memory than the Yee algorithm because fewer field elements are involved in computation. Numerical examples are provided to validate its accuracy and effectiveness

The characteristics of the typical microstrip discontinuities, such as right-angle bends, T junctions and steps in width, are investigated based on the Finite-Difference Time-Domain (FDTD) method in a wide-frequency range. The compensation methods of the microstrip discontinuities are also discussed and compensated discontinuities can improve the circuit performance as well as the bandwidth compared with the uncompensated. The electric field varying with signal traveling in the spatial and time domain at the microstrip discontinuities are also presented.

Various methods are available at the disposal for computing the solution of electromagnetic problems expeditiously. Electromagnetic scattering problems can be classified into two broader categories named as surface and volume problems. These problems can be solved using differential and integral equations. Differential equations based techniques use Finite Element Method (FEM) and Finite Difference Time Domain (FDTD) methods and major integral formulation based technique is Method of Moment (MOM). Any set of linear equations for a given system can be solved using direct or iterative methods. Direct solvers confront many computational complexities and use large amount of memory while iterative solvers reduce computational complexities and use less amount of memory. In this research work some integral equations based solver schemes such ass Finite Element Method (FEM), Finite Difference Time Domain Method (FDTD) and Method of Moments (MOM) for surface and volume scatters are discussed and results are compared. The comparison is with respect to complexity and memory requirements for different solution schemes.

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

The finite-difference time-domain (FDTD) method as realized in the Yee algorithm is very useful for solving the analytically intractable diffraction problems that arise in the design of diffractive optical elements (DOE). The error, e, of the Yee algorithm is rather large. We introduce a new high accuracy version of the Yee algorithm based on nonstandard finite differences. We have verified its performance by comparing with known analytical solutions. We have used this algorithm to study the near field (0 - 10 wavelengths) diffraction patterns of three binary phase gratings. Grating (1) has a constant period, while grating (2) has a variable one. Grating (3) is generated by interlacing grating (1) with (2). The period of grating (1) is on the order of a wavelength. Some of these computed fields display interesting and possibly useful Fourier spectra.

In order to study the propagation characteristics of Ultra High Frequency (UHF) signals excited by partial discharge in an actual power transformer, a simulation model of the power transformer is established using Finite Difference Time Domain (FDTD) method to simulate the propagation progress of the UHF signals. The receiving signals in different points and planes are analyzed by time domain and frequency domain methods. The results show that due to the complicated structure, the magnitude of the receiving signals vary greatly with places and the distribution of energy also varies very much. The higher the frequency, the greater the attenuation.

A finite difference time domain (FDTD) method in combination with the perfectly matched layer (PML) is used for dispersive media. The FDTD method is derived using the convolution relationship between the current density J and the electric field E. The high accuracy of the FDTD method is confirmed by computing the reflection and transmission coefficients for a one dimensional nonmagnetized plasma slab.

The finite difference time domain (FDTD) method is considered a prominent approach in computational electromagnetics for the wave propagation analysis of closed geometries in time domain. However, since this uses a structured mesh, the staircase approximation at the curved boundaries is a computational challenge in FDTD. Recently, meshless methods based on radial point interpolation method (RPIM) on unstructured mesh have gained importance in electromagnetic simulations due to their capability of modeling arbitrary shaped geometries. In the RPIM, the field variable at a node is interpolated by the values at the surrounding nodes which fall in the support domain. After assembly, this results in a banded matrix of size N χ N, where N is the total number of mesh cells. The computational cost of solving this is high for large structures. On the other hand, FDTD is a simple method in which the field variables are directly calculated using update equations. So, the FDTD and Meshless RPIM methods can be combined to model structures with partial curved geometries, with meshless RPIM method at the curved regions and the Cartesian FDTD for the rest of the domain. To validate the method numerically, a WR-229 90 degree waveguide bend is modelled using meshless method at the curved region and FDTD at the straight waveguide regions. Gaussian radial basis functions are used for the interpolation and to generate the shape function matrices in the meshless region. Interface matching conditions for the electric and magnetic fields are matched across the interface boundaries. The external domains are truncated with 2nd order MUR absorbing boundary conditions. The results of the hybrid approach are compared with those from the regular FDTD, with the Meshless approaches and the improvement in the computational cost is reported.

The numerical dispersion is one of the main factors to affect the accuracy of the finite-difference time-domain (FDTD) method. It can be easy to be taken for granted that a smaller time step leads to smaller simulation errors. This paper reveals that smaller time steps do not always make more accurate results in FDTD simulations. We analytically investigated how time steps affect the numerical dispersion of two FDTD methods: the leapfrog FDTD(2,2) method and the FDTD(2,4) method. The investigations in this paper show that in the FDTD(2,2) method, a larger time step limited by the Courant-Friedrichs-Lewy (CFL) condition is more helpful to reduce the numerical dispersion error. However, in the FDTD(2,4) method, as the time step grows, the numerical dispersion error decreases at the beginning and then increases. Several numerical examples are carried out to verify our analysis.