Grid decoupling in finite element solutions for Maxwell's equations

Certain finite-element discretization methods used in time-domain electromagnetic modeling reduce to a type of finite-difference method when applied on a regular mesh. The form of this underlying finite-difference method is unusual; it consists of two decoupled grids, rotated 45° from the original finite element mesh     

A subgridding method for the time-domain finite-difference methodto solve Maxwell's equations

A modification to the time-domain finite-difference method (TDFDM) that uses a variable step size is investigated. The entire computational volume is divided into a coarse grid with a large step size. A fine grid with a small step size is introduced only around discontinuities. The corresponding time increments are related to the spatial increments with the same ratio in order to minimize the numerical dispersion. The fields within the coarse and fine grids are found using the TDFDM, while an interpolation in space and time is utilized to calculate the tangential electric field on the coarse-fine grid boundary. This subgridding decreases the required computer memory and therefore expands the capability of the TDFDM. The technique is shown to be numerically stable and does not entail any extra numerical error. The method is applied to the calculation of waveguides and microstrips     

Spectral Lanczos decomposition method for time domain and frequencydomain finite-element solution of Maxwell's equations

A technique that combines the spectral Lanczos decomposition method and the finite-element method is introduced that can be used to solve Maxwell's equations in both the frequency and time domains. The present technique is an implicit, unconditionally stable finite-element time and frequency domain scheme. The Lanczos process is implemented only at the largest time or frequency of interest. The efficiency and effectiveness of this new technique are illustrated by using the numerical example of a three-dimensional dielectric-loaded cavity resonator     

The time domain Green's function and propagator for Maxwell's equations

The free space time domain propagator and corresponding dyadic Green's function for Maxwell's differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Green's function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygen's principle cannot be satisfied. To illustrate the value of this Green's function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.     

A domain decomposition finite-difference method for parallelnumerical implementation of time-dependent Maxwell's equations

A domain decomposition technique together with an implicit finite-difference scheme is used to design a parallel algorithm to solve for electromagnetic scattering in the time-domain by an infinite square metallic cylinder. The implicit difference scheme yields second-order accuracy, unconditional stability, and at each time step, a large system of linear equations. The domain decomposition technique reduces the solution of this large system to that of many independent smaller subsystems. The present algorithm can be easily implemented on coarse-grain parallel vector supercomputers to obtain a speedup close to the number of available central processing units (CPUs)     

Improving the Newmark time integration scheme in finite element time domain methods

The Newmark formulation for the time-stepping solution of the electric field vector wave equation is modified in order to suppress low-frequency spurious responses. It is verified that the proposed method has the advantage of halving the number of iterations necessary to solve the system of linear equations and it is shown that setting the number of iterations per time step can be more convenient than establishing a residual tolerance to verify convergence. In addition, the use of diagonal and incomplete Cholesky preconditioners are tested through numerical examples and they appear to be equivalent in terms of CPU time, leaving the first as the preferable choice concerning memory storage and programing facilities.     

三维时域有限元-边界元方法中奇异积分计算

研究三维时域有限元一边界元混合方法中奇异积分的计算.将其中的一些积分进行等价变形以降低奇异性.并给出了积分等价变形过程中所遇到的数值错误的一种解决方法,这一数值错误与时域有限元一边界元方法中的固有处置有关.讨论了频域中格林函数奇异点提取法推广应用于时域混合方法中奇异积分的计算,指出,频域中奇异点提取法的一些处理不适宜于时域奇异积分.数值实验检验了所给处理方法.     

Hybrid technique combining finite element, finite difference andintegral equation methods in time domain

A new hybrid time domain method is presented which combines three well-known numerical techniques. i.e. the finite difference time domain (FDTD) method, finite element (FE) method and method of moments (MoM). The hybrid scheme has been designed to handle complex geometries comprising arbitrary thin-wire structures and inhomogeneous dielectric regions the shape of which can also be arbitrary. Numerical results are presented which illustrate the accuracy of the method     

Point-matched time domain finite element methods for electromagnetic radiation and scattering

Direct time domain computation of Maxwell's differential equations will soon become a practical technique because of the availability of supercomputers. The principal methods used in time domain computations and the supporting theories are presented. The point-matched finite element method is chosen as the main feature of this presentation, which includes the discretization of equations, conforming mesh generation, dielectric and metallic interfaces, numerical stability and simulation of radiation conditions. Numerical results of scattering of Gaussian pulses are presented in time sequences.     

A local mesh refinement algorithm for the time domain-finitedifference method using Maxwell's curl equations

An efficient local mesh refinement algorithm, subdividing a computational domain to resolve fine dimensions in a time-domain-finite-difference (TD-FD) space-time grid structure, is discussed. At a discontinuous coarse-fine mesh interface, the boundary conditions for the tangential and normal field components are enforced for a smooth transition of highly nonuniform held quantities     

A comparison of transient solutions of Maxwell's equations to thatof the modified Maxwell's equations

In 1986 H.F. Harmuth introduced a modification of Maxwell's equations to study the propagation of transient electric and magnetic field strengths in lossy media. Opponents of this modification of Maxwell's equations have claimed and attempted to demonstrate that Maxwell's equations in their known forms can correctly be solved, for example by the Laplace transformation method, to obtain solutions of transient electric and associated magnetic field strengths in lossy media without encountering any difficulties. This work presents detailed computer plots of Harmuth's transient solutions of the modified Maxwell's equations and that of Maxwell's equations solved by the Laplace transformation characteristic for the two solutions, which indicate that they are not the same. It is shown that Harmuth's procedure results in physically more plausible solutions     

Application of biorthogonal interpolating wavelets to the Galerkinscheme of time dependent Maxwell's equations

A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwell's equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verifications on some resonant structures     

FDTD法计算高频单极天线特性

用时域有限差分法（Ｆｉｎｉｔｅ Ｄｉｆｆｅｒｅｎｃｅ Ｔｉｍｅ Ｄｏｍａｉｎ Ｍｅｔｈｏｄ）计算天线阻抗特性,可以使用不同的激励方式,文章比较了采用不同激励方式时,天线的输入阻抗。文中的主要内容是将表面阻抗法用于ＦＤＴＤ中,计算架设在介质平面上单极天线的辐射特性,并用ＦＤＴＤ法计算了介质平面上铺设不同尺寸的导体平面时,单极天线的输入阻抗随导体平面尺寸变化的特性。     

Conformal hybrid finite difference time domain and finite volumetime domain

A hybrid method that combines the finite difference time domain (FDTD) and the finite volume time domain (FVTD) methods is presented. The FVTD, based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer, and the FDTD is used to model the fields in the surrounding area. The two are coupled together through interpolation. The vertex-based FVTD allows for more convenient and accurate interpolations than a conformal FDTD method. The hybrid method is validated through two examples-the scattering by a PEC cube and sphere-by comparison with the direct FDTD solution, and with an exact Mei series solution for the spherical case     

新型分裂步长时域有限差分法

提出一种新型的分裂步长时域有限差分(NSS-FDTD)法,并对其数值色散进行分析。该方法基于Split-Step方案和Crank-Nicolson方案,采用新的矩阵分解形式,与传统的FDTD算法、SS-FDTD算法相比,减少了计算复杂度。新型算法的推导程序简单,且具有良好的数值色散特性,还加入了一阶Mur吸收边界条件,给出一阶Mur吸收边界差分方程。将数值实验的结果和传统FDTD方法及理论值进行比较,数值结果一致性较好。     

Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.     

A hybrid time-domain technique that combines the finite element, finite difference and method of moment techniques to solve complex electromagnetic problems

This paper describes a hybrid technique directly operating in time domain that combines the finite element time domain (FETD), the finite-difference time-domain (FDTD) and the integral-equation-based method of moments in the time domain (MoMTD) techniques to analyze complex electromagnetic problems involving thin-wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary. The method brings together the ability of the FDTD scheme to deal with arbitrary material properties, the versatility of the FETD to accurately model curved geometries, and that of the MoM to analyze thin-wire structures. Working in the time domain provides wide-band information from a single execution of the marching-on-in-time procedure and simplifies the interfacing of the FE and MoM methods with the FDTD, an approach specifically designed for time domain analysis. Numerical results that validate the hybrid method and show its capabilities are presented in the paper.     

3D crank-nicolson finite difference time domain method for dispersive media

The unconditionally stable Crank-Nicolson finite difference time domain (CN-FDTD) method is extended to incorporate frequency-dependent media in three dimensions. A Gaussian-elimination-based direct sparse solver is used to deal with the large sparse matrix system arising from the formulation. Numerical results validate and confirm that the scheme is unconditionally stable for time steps over the Courant-Friedrich-Lewy limit of classical FDTD.     

Simultaneous time and frequency domain solutions of EM problemsusing finite element and CFH techniques

This paper describes an efficient method for both time- and frequency-domain solutions of electromagnetic (EM) field problems. In this method EM field problems are formulated using Laplace-domain finite element approach and are solved using complex frequency hopping (CFH) technique. CFH is a moment-matching technique which has been used successfully in the circuit simulation area for solution of large set of ordinary differential equations. Problems consisting of Dirichlet, Neumann and combined boundary conditions can be solved using the proposed algorithm to obtain both time and frequency responses. Several electromagnetic field problems have been studied using the new technique and the speed-up advantage (one to three orders of magnitude) compared to conventional finite element technique is demonstrated. A good agreement between numerical results obtained using the proposed method and the previously published results has been found     

Modelling of coaxial-fed microstrip patch antenna by finite difference time domain method

A direct three-dimensional finite-difference time-domain (FDTD) method is applied to coaxial-fed microstrip antennas. The model is shown to be an efficient and accurate tool for modelling coaxial-fed structures. The reflection coefficient can be determined from the simulated time-domain wave that is reflected down the coaxial line. Excellent agreement over a wide frequency range is shown in two cases between the measured and FDTD derived results.<>