Hopf solutions of Maxwell equations: analysis and simulation by FDTD

The finite-difference time domain (FDTD) method is a numerical technique based on the finite difference concept. It is employed to solve Maxwell's equations for the electric and magnetic field distributions in both the time and spatial domains. The FDTD method utilizes the central difference approximation to discretize two of Maxwell's curl equations, namely, Faraday's and Ampere's laws, in both the time and spatial domains, and then solve the resulting equations numerically to derive the electric and magnetic field distributions at each time step and spatial point using the explicit leap-frog scheme. The FDTD solution, thus derived, is second-order accurate, although the difference formulation is first order, and is stable if the time step size is chosen to satisfy the special criterion.

9 - Computational Electromagnetics: The Finite-Difference Time-Domain Method

Hybrid finite element (FE) solutions of transient electromagnetic field are proposed. Time dependent Maxwell's curl equations are solved separately using edge elements for the electric field approximation and nodal-based elements for the magnetic field approximation. Two different formulations are presented: the first adopts a unique mesh, the second two complementary FE meshes. The solution of the resulting equations systems is performed by explicit methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Summary form only given. We present our recent results on the calculation of the distribution of the light scattered by red blood cells in the full range of scattering angle between 0 to 180 degrees using an accurate quantitative finite-difference-time-domain (FDTD) method. The FDTD algorithm allows computation of scattering from cells of any shape and with any index of refraction profile. The algorithm discretizes Maxwell's curl equations in space and time, resulting in a set of explicit finite-difference equations.

A numerical method for predicting the sinusoidal steady-state electromagnetic fields penetrating an arbitrary dielectric or conducting body is described here. The method employs the finite-difference time-domain (FD-TD) solution of Maxwell's curl equations implemented on a cubic-unit-cell space lattice. Small air-dielectric loss factors are introduced to improve the lattice truncation conditions and to accelerate convergence of cavity interior fields to the sinusoidal steady state. This method is evaluated with comparison to classical theory, method-of-moment frequency-domain numerical theory, and experimental results via application to a dielectric sphere and acylindrical metal cavity with an aperture. Results are also given for a missile-like cavity with two different types of apertures illuminated by an axial-incidence plane wave.

Finite-difference time-domain (FDTD) method is a direct solution of Maxwell differential equations. It changes the Maxwell curl equations that involve time variable to the difference equations in the gridding space, and changes all kinds of problems to the initial problems, and this change reflects all the time specialty of the electromagnetic wave, so the FDTD method can settle electromagnetic dispersion and electromagnetic radiation of the complex objects and the objects of heterosphere. Here the radiation fields of coaxial cable with one slot, three and five vertical slots are simulated, and set the base for research on the radiation field of the whole leaky coaxial cable.

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 difierential wavelet-based operator deflned on an interval is presented and used in evaluating the electromagnetic fleld described by Maxwell's curl equations, in time domain. The wavelet operator has been generated by using Daubechies wavelets with boundary functions. A spatial difierential scheme has been performed and it has been applied in studying electromagnetic phenomena in a lossless medium. The proposed approach has been successfully tested on a bounded axial-symmetric cylindrical domain.

SUMMARYIn this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi‐stationary Maxwell's curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless particle model has provided good results in agreement with the analytical ones and by overcoming the drawback of the mesh generation. The numerical model has been validated, at first, in computing the electric potential and the external magnetic field for a dipole plunged near the upper surface of a homogeneous sphere simulating the human brain. Simulation results obtained by simulating two concentric spheres with different conductivities are also reported. Moreover, in order to better assess the validity of the proposed approach, a realistic human brain cortex model has been also simulated and compared with boundary element method results. A satisfactory agreement has been reached. Copyright © 2012 John Wiley &amp; Sons, Ltd.

In this paper an efficient algorithm is presented for the development of compact and passive macro‐models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of finite elements. The proposed methodology is founded on a new finite element formulation that casts Maxwell's curl equations in a state‐space form. Such state‐space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the finite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation efficiency can be avoided by a proper selection of the finite element expansion functions used for the discretization of the electromagnetic fields. More specifically, it is shown that the proper selection of expansion functions renders the state‐space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector finite elements. This equivalence is then used to effect Krylov‐based model order reduction directly from the finite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macro‐modelling algorithm is demonstrated through its application to a variety of microwave passive components. Copyright © 2002 John Wiley &amp; Sons, Ltd.

The time-harmonic Discontinuous Galerkin Method (DGM) is a flexible forward solver for inverse scattering problems in electromagnetics. Standard DGM discretizations of Maxwell's curl equations, simultaneously solving for both electric and magnetic fields, are generally more accurate but less efficient than the DGM applied to the electric vector wave equation. A natural extension is to mix DGM formulations such that either the curl equation formulation or the wave equation formulation is locally adopted to preserve accuracy. Herein we present such a mixed DGM formulation for time-harmonic scattering problems, where the formulation choice is locally based on the presence of electric or magnetic constitutive parameters that differ from the background medium.

With the advent of reliable sources of ultrashort optical pulses, photoconductive switches, photoconductive sampling have been turned into methods that allow one to generate and to detect ultra-fast electric pulses. Experiments have shown that commuting devices of optoelectronic pulses associated with appropriate antennas can be used to generate, control and detect picosecond bursts of electromagnetic radiation. It leads to various applications such as using the transient radiation properties of antennas for the characterization of materials by coherent microwave transient spectroscopy. This paper deals with an electromagnetic analysis of these exponentially tapered coplanar stripline antennas. In particular, the purpose of this electromagnetic study is to understand the radiation mechanism of this antenna type and to optimize it. For this analysis and for the considered frequency bands, the finite difference time domain (FDTD) method is a suitable method because it takes all the propagation and radiation modes into account. The FDTD method based on a discrete form of Maxwell's equations leads directly to the time evolution of the radiated field.

The scattering characteristics of the planar array composed of impedance terminated dipoles and a finite reflector are studied by finite difference time domain (FDTD) method. The current distribution on the dipoles and the radar cross section (RCS) of the array are calculated and analyzed. It is seen that the array with resistor terminated dipole tends to give lower RCS.

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.