Fast Numerical Techniques Based Analysis of Electromagnetic Problems Using MATLAB

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.

This work introduces a conformal finite difference time domain (CFDTD) method to accurately determine the dispersion relation of an A6 relativistic magnetron. The accuracy is measured by comparing with accurate SUPERFISH calculations based on finite element method. The results show that an accuracy of 99.4% can be achieved by using only 10,000 mesh points with Dey-Mittra algorithm. By comparison, a mesh number of 360,000 is needed to preserve 99% accuracy using conventional FDTD 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.

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 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.

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 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.

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

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 analyze the switching transient electromagnetic fields generated by the aerial busbars in substation, the one-dimensional (1-D) time domain finite element (TDFE) method is presented to analyze the transient wave process in multi-conductor transmission lines (MTLs) with branches. Based on the Pade's approximation and on Prony's method, the iterative equations of the aerial MTLs are reported. Iterative formulae are also presented to determine the boundary conditions at the nodes of the branches in this paper. The proposed method avoids the Gibbs effect of the finite difference time domain (FDTD) method. An aerial busbars model in a 500 kV substation is analyzed when circuit breakers and disconnect switches are closed. The numerical results are in good agreement with those calculated by Bergeron's method and FDTD method.

A recommended practice for computational electromagnetics (CEM) applied to the modeling and simulation of antennas (IEEE P2816) is currently being developed by the IEEE Antennas and Propagation Standards Committee (APS/SC). Four commonly adopted CEM solvers to simulate antenna problems are considered in this document: integral equations and method of moments (MoM), finite element method (FEM), finite difference time domain (FDTD) method and transmission line matrix (TLM) method. A broadband biconical antenna was also proposed and included as a benchmark problem that was tackled as an international interlaboratory comparison with twenty sets of results obtained using the different solvers. Overall a good agreement was observed with some deviating results, especially at the lower end of the frequency band. Herein this biconical antenna is numerically analyzed and the results compared with the analytical solution in an aim to explain the deviating results.

Context. Today, there is a rapid expansion of the range of modern branches of science and technology, which actively use satellite telecommunication systems to receive, process and transmit various information. These radioelectronic systems quite often require an increase of the volumes of information, which they are processing and transmitting. Increase of the volumes of transmitted information in two times can be achieved by using dual-polarization antenna systems and devices. Nowadays, most part of the specialists, who are engaged in the development of various modern polarization-processing microwave devices, carry out their numerical modeling and optimization using variational techniques, methods of integral equations, method of fields matching in partial regions. The methods with division of the internal region of the device into elementary cells are applied most actively. Among them in the time domain the most often used approach is finite difference method with the decomposition at hexagonal mesh, while and in the frequency domain the finite elements method with the adaptive tetrahedral mesh is applied. Therefore, the estimation of the speed and accuracy of these methods with the purpose of determination of more effective among them is a relevant problem. Objective. The goal of the research is comparison of speed and accuracy of the calculations of electromagnetic characteristics of waveguide polarizers using FEM and FDTD methods, as well as the comparison of the convergence of these methods for the analysis of polarization-processing microwave devices with diaphragms. Method. For the calculations and analysis of electromagnetic characteristics in the article we used the method of finite differences in the time domain (FDTD) and the method of finite elements in the frequency domain (FEM). In FEM the volume is split into the tetrahedral mesh cells. In FDTD the computational domain is divided into hexagonal mesh cells. Results. It was found that the convergence of voltage standing wave ratio for the waveguide polarizer is fast for both methods. It was obtained that the convergence of the characteristics of differential phase shift, axial ratio, and crosspolar discrimination of the developed microwave device turned out to be much more sensitive to the number of mesh cells used. Moreover, in the research it was obtained by calculations that the computation time by the finite elements method in the frequency domain is more than 2 times less than the corresponding time required for calculations by the finite difference time domain method. When using the finite elements method in the frequency domain the corresponding number of tetrahedral mesh cells is 10 times less than the number of hexagonal mesh cells, which are used in the finite difference time domain method. Conclusions. Performed investigations have shown that FEM in the frequency domain, which applies an adaptive tetrahedral mesh, is more efficient than the FDTD method for the calculations of phase and polarization characteristics of modern waveguide polarizers and other microwave devices for various applications.

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.

Computation of effective propagation parameters in the optical domain with a finite difference time domain method

In the analysis of antennas and scattering problems by the finite difference time domain (FDTD) method, the dimensions of the problem space are primarily determined by the quality of the radiation boundary condition (RBC) that is used to truncate the computational grid. Higher order boundary conditions give better performance when used in conjunction with pulse type sources. Unfortunately, they are less efficient when applied to scattering problems as shown by Blaschak and Kriegsmann (1988). This suggests that the current one-way wave equation approximations are overlooking an important aspect of the problem. We believe that the problem resides in the inability of the higher order approximations to deal with the evanescent part of the field. Since this evanescent part is much more prominent in scattering type problems, especially at low frequencies, this would explain the apparent failure of the higher order conditions in those cases. We propose a boundary condition that takes into account evanescent as well as non-evanescent plane waves and prove that this new RBC gives excellent results in both scattering and pulse-type problems. We restrict ourselves to two-dimensional problems but our approach can be extended to 3D problems as well.