Time domain global modelling of EM propagation in semiconductor using irregular grids

A two‐dimensional finite volume time domain (FVTD) method using a triangular grid is applied to the analysis of electromagnetic wave propagation in a semiconductor. Maxwell's equations form the basis of all electromagnetic phenomena in semiconductors and the drift‐diffusion model is employed to simulate charge transport phenomena in the semiconductor. The FVTD technique is employed to solve Maxwell's equations on an irregular grid and the finite box method is implemented on the same grid to solve the drift‐diffusion model for carrier concentration. The locations of unknowns have been chosen to allow linking coupled Maxwell's equations and transport equations in a seamless way. To achieve suitable accuracy and computational efficiency, using irregular grid topology allows a finer mesh in doped region and at junction, and a coarser mesh in substrate and insulting regions. The proposed scheme has been implemented and verified by characterizing electromagnetic wave propagation at microwave frequency in a semiconductor slab with arbitrary doping profile. Copyright © 2002 John Wiley & Sons, Ltd.     

Simulation of EM wave propagation in magnetoelectric media using TLM

In this paper, the simulation of general frequency‐dependent magnetoelectric material properties in time‐domain TLM is described. The formulation is developed from Maxwell's equations and the constitutive relations using bilinear 𝒵‐transform methods leading to a general Padé system. The approach is applicable to all frequency‐dependent linear materials including those displaying anisotropic and bianisotropic behaviour. The method is validated by the example of a chiral slab having an analytic solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Body fitted grid generation with moving boundary and its application for dielectric waveguides

The stress birefringence and mode coupling effects in polarization-preserving fibres are most important problems which need to be improved. For a realization of some optical devices, the dielectric waveguide with sinusoidally varying circular cross-section has been investigated. It becomes very important to analyse the electromagnetic field distribution in a dielectric waveguide with a time-dependent moving boundary. This paper shows that numerical methods can simulate the effect of the external disturbance on the dielectric waveguide from time to time. The author has discussed body fitted grid generation with moving boundary for the Poisson and Laplace equations.^1,2 We have extended this technique for Maxwell's equation. The technique employs a kind of an expanded numerical grid generation. As the author adds the time component to grid generation, the time dependent co-ordinate system which coincides with a contour of moving boundary can be transformed into a fixed rectangular co-ordinate system. We could show the electric distribution in the waveguide time by time to verify the possibility of an application for an optical fibre. This technique makes it possible not only to analyse the effect of the external disturbance in a coherent optical communication system but also to fabricate optical devices.     

Delaunay–Voronoi surface integration: a full‐wave electromagnetics discretization for electronic device simulation

A promising time domain electromagnetics numerical method for treating the highly nonlinear problem of charge transport in electronic devices called Delaunay–Voronoi surface integration is presented. This method couples the rotational electric and magnetic fields governed by Ampere's and Faraday's laws with the electrostatic potential dictated by Poisson's equation in a simultaneous solution. Discretization of the governing equations using dual meshes and the relevant boundary conditions are presented. The engineering application details specific to electronic device simulation are treated, and an example calculation is shown to compare with an analytical solution for propagation in a waveguide. Benchmark results are presented for the rotational equations, Poisson's equation, and the complete set of electromagnetic equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhanced distributed computing message passing strategies for FDTD

The finite difference time domain method (FDTD) solves Maxwell's equations by employing numerically and storage intensive computation to map the electric and magnetic fields within a finite volume as an explicit function of time. Distributed computation, using heterogeneous networks of computers, is a cost‐effective way of applying FDTD; however interprocessor communication is the rate‐limiting step. In particular, in most laboratories there is a surplus of unused, desktop CPU cycles during the evening and night. We have investigated ways of utilizing this resource by examining various communication harnesses for distributed computing and have for the first time in a distributed FDTD EM application, employed data packing mechanisms to alleviate the bottleneck caused by network latency and limited bandwidth availability. Copyright © 1999 John Wiley & Sons, Ltd.     

Consistent finite difference modelling of Maxwell's equations with lossy symmetrical condensed TLM node

A propagator integral interpretation for general TLM processes is presented and applied to discretized Maxwell's equations. The approach provides exact algebraic solutions of finite difference equations along a quite universal scheme. Specifically, Johns's process based on the symmetrical condensed node is reconstructed and generalized as a clear-cut FD algorithm. The fields computed are exact time-domain solutions of the FD equations, provided that total voltages and currents are evaluated and stub quantities are not externally excited. Losses are very naturally incorporated into the TLM algorithm. The structural similarity of the TLM process (properly operated) with the propagator integral appears just as fundamental as general and should have further applications.     

An improved smoothed particle electromagnetics method in 3D time domain simulations

In this paper, an enhanced variant of the meshless smoothed particle electromagnetics (SPEM) method is performed in order to solve PDEs in time domain describing 3D transient electromagnetic phenomena. The method appears to be very efficient in approximating spatial derivatives in the numerical treatment of Maxwell's curl equations. In many cases, very often, accuracy degradation, due to a lack of particle consistency, severely limits the usefulness of this approach. A numerical corrective strategy, which allows to restore the SPEM consistency, without any modification of the smoothing kernel function and its derivatives, is presented. The method allows to restore the same order of consistency for both interior and the boundary regions outperforming the original version of SPEM as far as accuracy and stability are concerned. Therefore, computational details are reported and simulations, using uniform and non‐uniform particles distribution in 3D domains, are performed for the first time in order to validate the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Efficient implementation issues of finite difference time-domain codes for Maxwell's equations

The computer implementation of time-domain finite difference methods for the solution of Maxwell's equations is considered. As the basis of this analysis, Maxwell's equations are expressed as a system of hyperbolic conservation laws. It is shown that, in this form, all the well-known differencing schemes can be easily expressed, thus increasing the applicability of the implementation issues to be discussed. Practical issues, such as computational efficiency and memory requirements, are discussed for the implementation of the finite difference schemes. Advanced programming techniques in the C language are used to implement the finite difference schemes discussed. The example of the penetration of electromagnetic energy through a shield with a thick gap is used to check the performance of the methods. It is shown that, for cases where the disturbance remains localized in the computational mesh, these techniques result in memory and CPU time savings.     

An overlapping Yee finite‐difference time‐domain method for material interfaces between anisotropic dielectrics and general dispersive or perfect electric conductor media

A novel stable anisotropic finite‐difference time‐domain (FDTD) algorithm based on the overlapping cells is developed for solving Maxwell's equations of electrodynamics in anisotropic media with interfaces between different types of materials, such as the interface between anisotropic dielectrics and dispersive medium or perfect electric conductor (PEC). The previous proposed conventional anisotropic FDTD methods suffer from the late‐time instability due to the extrapolation of the field components near the material interface. The proposed anisotropic overlapping Yee FDTD method is stable, as it relies on the overlapping cells to provide the collocated field values without any interpolation or extrapolation. Our method has been applied to simulate electromagnetic invisibility cloaking devices with both anisotropic dielectrics and PEC included in the computational domain. Numerical results and eigenvalue analysis confirm that the conventional anisotropic FDTD method is weakly unstable, whereas our method is stable. Copyright © 2013 John Wiley & Sons, Ltd.     

Absorbing boundary conditions for the FD‐TLM method : the perfectly matched layer and the one‐way equation technique

This paper investigates the absorbing boundary conditions for the frequency domain transmission line matrix method. Two approaches are presented, namely the perfectly matched layer (PML) technique and the one‐way wave equation. Concerning the PML technique, two‐dimensional and three‐dimensional transmission line matrix (TLM) nodes, already used in time domain, are exploited in frequency domain where a rigorous formulation of these PML–TLM nodes is presented. In addition, two types of one‐way wave operators are also transposed from time to frequency domain TLM approach: Taylor expansion and Higdon's boundary conditions. The simulation of a wideband matched load WR‐28 rectangular waveguide is presented for validation. Excellent results are obtained with a very thin PML layer. Results concerning one‐way operator techniques also show very good return loss performances. For instance, Higdon's boundary condition was extended beyond third‐order approximation, and a return loss better than 160 dB was obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison of numerical methods for the full‐wave analysis of flange mounted rectangular apertures

The analysis and design of small‐ and medium‐sized aperture antenna arrays is an important task in the development of many microwave systems, and is computationally heavy due to the typical requirements for efficiency and accuracy. Several approaches have already been proposed in the literature, but they have not been compared so far in terms of their computational efficiency. In this paper, we compare different methods, either based on rectangular waveguide modes to expand the field over the aperture, or based on Gegenbauer's polynomials for singular fields representation. Their numerical properties are studied, and their performance compared. It is concluded that similar accuracies are achieved, whilst the approach using the spectral‐domain rectangular waveguide mode formulation is the more robust, and should be considered for the development of general purpose software packages. Copyright © 2000 John Wiley & Sons, Ltd.     

计算非线性时变涡流场的有限元方程频域算洁

本文提出了一种计算时变非线性涡流场的有限元方程频域算法，该方法在时域内确定非线性单元各时刻的磁阻率，利用离散付立叶变换在频域内求解有限元方程，并用直接解法与逐次松驰因子迭代法相结合的方法处理频域方程组的非线性问题。文中还用一算例验证了本法的有效性。     

Finite deffernce time-domain approximation of Maxwell's equations with non-orthogonal condensed TLM mesh

A convex hexahedral TLM mesh of arbitrary shape is presented and the transmission-line matrix method extended to any non-orthogonal configuration. The novel mesh constitutes a natural generalization of Johns' condensed node. The associated TLM process is analysed and reconstructed as a genuine finite difference time-domain algorithm. Nodal S-parameters are derived from discretized Maxwell's equations and canonical stability criteria yield the TLM timestep. Unitarity is discussed and energy conservation confirmed in the non-conductive case. A given block-diagonal representation of the S-matrix restrains processing time per node and iteration within the range of traditional methods. The shortcomings of the rigid classical grid, as the need for inaccurate staircasing approximations, are, however, ruled out. Our analysis takes advantage of the recently developed propagator integral approach.     

A new a priori ordering method for sparse systems of equations based on an ordered output set

In the context of solution to the sparse systems of equations arising in computer-aided analysis and design of electrical networks using the Gaussian elimination (GE) process it is well-known that an a priori reordering for equations and unknowns is almost mandatory. In this paper we present a new approach for a priori ordering for the equations and unknowns using the theory of output sets. Our approach yields an ordered output set as the pivot sequence for an associated GE process. Our algorithm is simple and is more general than the existing ones and leads to an s-minimal GE process. An example is presented for illustrating the algorithm and the computational complexity of the new method has been analysed. Additional work needed in the area is indicated.     

Numerical study of the effect of defect layer on unmagnetized plasma photonic crystals

In this paper an explicit finite-difference time domain scheme developed in staggered grids is used to solve the Maxwell’s equations in Drude medium. Besides the preservation of discrete zero-divergence condition in electric and magnetic fields, we also aim to conserve the inherent conservation laws in simple medium all the time using the temporally second-order accurate explicit symplectic partitioned Runge-Kutta scheme. Within the framework of a semidiscretized method, the first-order spatial derivative terms in Faraday’s and Ampère’s equations are approximated to get an accurate numerical dispersion relation equation. The derived numerical angular frequency is accurately related to the wavenumber of Maxwell’s equations for the space centered scheme of fourth-order accuracy. The resulting symplectic finite difference scheme developed in the time domain minimizes the difference between the exact and numerical group velocities. This newly proposed scheme is applied to model EM waves in the unmagnetized plasma crystal which contains a defect layer in photonic crystal. Our purpose is to numerically study the effects of defect layers on the propagation insight.     

Numerical optimization of a waveguide transition using finite element beam propagation

We consider a waveguide with principal guiding direction for which the beam propagation method is applicable. A simulation method based on an FEM for Maxwell's equation with 3D Nedelec elements is developed. The power loss of the waveguide is minimized by varying a finite number of shape parameters. We validate the method by comparing our findings to some published results. Copyright © 2014 John Wiley & Sons, Ltd.     

频域紧支撑正交小波及其在暂态保护中应用

小波分析作为时频分析工具已经越来越广泛地应用于电力系统的各个领域，如何选择和构造最适合用户需要的小波具有重要意义。从信号的时频分析角度，频域紧支撑小波比时域紧支撑小波具有更好的分频效果，然而其时域的衰减性较差，介绍了构造频域紧支撑小波的一般方法，分析了频域是支撑小波的性质，并在Meyer小波基础上提出了构造理想分频效果并且具有任意阶衰减及满足各种相频响应需要的频域紧支撑正交小波，模拟暂态信号的小波分析结果表明，该小波的分频效果和计算的有效性是令人满意的。     

The discrete time domain Green's function or Johns matrix — A new powerful concept in transmission line modelling (TLM)

A new TLM-based concept analogous to the Green's function approach in classical electromagnetic theory is presented. It employs the procedure known as time domain diakoptics. The response of a TLM mesh to a unit impulse excitation at selected input points is interpreted as a discrete Green's function in the time domain, and the term ‘Johns matrix’ is proposed for this characteristic response. As in classical theory, the response of the mesh to an arbitrary excitation is found by convolving the excitation with its Johns matrix. This concept extends the generalized scattering parameter concept into the time dimension, opens unprecedented possibilities for partioning time domain problems at the field level, and permits large-scale preprocessing of substructures for computer-aided design. It also represents and elegant way of modelling broadband absorbing boundary conditions, imperfectly conducting walls and general frequency dispersive boundaries in the time domain.     

An extended Huygens' principle for modelling scattering from general discontinuities within hollow waveguides

The modal fields, generalized scattering matrix (GSM) theory and dyadic Green's functions relating to a general uniform hollow waveguide are briefly reviewed in a mutually consistent normalization. By means of an analysis linking these three concepts, an extended version of the mathematical expression of Huygens' principle is derived, applying to scattering from an arbitrary object within a hollow waveguide. The integral‐equation result expresses the total field in terms of the incident waveguide modal fields, the dyadic Green's functions and the tangential electromagnetic field on the surface of the object. It is shown how the extended principle may be applied in turn to perfect conductor, uniform material and inhomogeneous material objects using a quasi method of moments (MM) approach, coupled in the last case with the finite element method. The work reported, which indicates how the GSM of the object may be recovered, is entirely theoretical but displays a close similarity with established MM procedures. Copyright © 2001 John Wiley & Sons, Ltd.