Finite-difference time-domain method for three-dimensional grid of hexagonal prisms

Recently, the present authors have applied the FDTD (Finite‐Difference Time‐Domain) method to acoustic problems. FDTD is one of the finite‐difference methods in the time domain used in electromagnetic problems. However, in this method, phase errors cannot be neglected in a large‐scale propagation analysis such as indoor acoustic propagation and they cause problems in the analysis. In order to reduce the phase error, Cole has invented the NS‐FDTD (Non‐Standard FDTD) method for electromagnetic problems. However, the numerical dispersion and stability condition are not described in Cole's paper. Also, the definition is given only for a cubic lattice. In this paper, an application of the three‐dimensional NS‐FDTD method to acoustic problems is attempted. Further, the method is extended to a rectangular lattice. The numerical dispersion and stability condition of the present method are derived. As a result, it is shown that the present method has much higher accuracy than the FDTD method. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(9): 15–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1115

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.

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.

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.

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 is a commonly used electromagnetic simulation method. However, in the analysis of electrically large structures with curved boundaries, the FDTD method suffers from cumulative errors introduced by inadequate resolution of curvature (stair-casing errors), reflection from absorbing boundaries, numerical dispersion, etc. On the other hand, integral equation based methods such as the method of moments (MoM) have available a wide variety of shape functions and grids for accurate resolution of the field on curved boundaries. We propose to hybridize the FDTD method and the MoM such that FDTD can be implemented on a relatively mesh, and the resulting crude solution employed as an initial guess to the solution of the MoM matrix equations using the conjugate gradient (CG) method.

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 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.

In this paper, a numerical approach based on weighted Laguerre polynomials finite-difference time-domain (WLP-FDTD) method is proposed to analyze noise coupling in power/ground planes between package and printed circuit board (PCB). Compared to the traditional finite-difference time-domain (FDTD) method, which is limited by Courant-Friedrich-Lecy stability condition, the proposed method has the unconditionally stable characteristic. Examples of a ball grid array package mounted on a PCB were simulated, and the numerical results show that the computation time of the proposed WLP-FDTD method can be 4.4% of that of the FDTD method at the same accuracy condition. Therefore, the proposed method has higher efficiency than the conventional FDTD method without sacrificing precision.

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.

Improved hybrid implicit–explicit finite-difference time-domain method with higher accuracy and user-defined stability condition

PV systems are considered one of the most important and popular forms of renewable energy sources worldwide. Due to the installation of PV modules on rooftops and outdoor areas, they are frequently subjected to lightning strikes, leading to a deterioration in PV systems. To provide an efficient lightning protection system, the accurate modeling of PV systems during lightning strikes is required. The main objective of this paper is to assess the transient behavior of PV systems when struck by lightning, where the PV system is modeled using the partial element equivalent circuit (PEEC) and finite difference time-domain (FDTD) methods. The PEEC method is one of the accurate methods used to represent the PV system by its equivalent RLC circuit to study lightning transients. Moreover, the FDTD method provides high accuracy when studying lightning transients by analyzing the electric and magnetic fields inside the PV system. The PEEC and FDTD methods are used to calculate the transient overvoltages at different points of the PV system. Then, a small-scale PV system is tested in the laboratory using an impulse generator representing the lightning strike to verify the correctness of the results obtained by simulation. Most of the existing research works introduce low accuracy in PV system modeling during lightning transients by neglecting the effect of the mounting system, metal frame, and mutual coupling, which are considered in this work. Moreover, the high-frequency nature of lightning current is considered when modeling the elements of the grounding system. Verifying the results by laboratory experiments can guarantee the application of the simulation model on large-scale PV systems.

In the present work, the analysis and design of a line fed two-layers coupled rectangular patch antenna is presented. The return loss, the input impedance, and the radiation pattern of the proposed structure are determined using the finite difference time-domain (FDTD) method. The effect of changing the air gap layer thickness between the two layers of that antenna is studied. The results obtained by the FDTD method are found to be in good agreement with the published data. Also it is found that as the air gap layer thickness is increased the 10-dB return loss bandwidth is decreased while the 3-dB beamwidth of that antenna is increased.

Finite-difference time-domain (FDTD) method is one of the most popular approaches to solve electromagnetic problems. Furthermore, an important application of FDTD method is that FDTD method can analyze the transient response of the microwave integrate circuits by incorporating the active and passive devices into simulation [1]-[4]. However, when the active devices are incorporated into the FDTD cell grids, the updating equations of the grids would become nonlinear due to the nonlinear voltage-current relations of the active devices. To solve these nonlinear equations, an iterative method such as Netwon-Raphson algorithm, need to be employed. This work presents a novel efficient approach for the incorporation of diodes into FDTD method without applying the iterative method. The large-signal model of a diode is combined with Yee's time-stepping equations to update the electric field by solving a quadratic equation. An example is presented to demonstrate the accuracy of this algorithm.