A quasi‐planar incident wave excitation for time‐domain scattering analysis of periodic structures

We present a quasi‐planar incident wave excitation for time‐domain scattering analysis of periodic structures. It uses a particular superposition of plane waves that yields an incident wave with the same periodicity as the periodic structure itself. The duration of the incident wave is controlled by means of its frequency spectrum or, equivalently, the angular spread in its constituting plane waves. Accuracy and convergence properties of the method are demonstrated by scattering computations for a planar dielectric half‐space. Equipped with the proposed source, a time‐domain solver based on linear elements yields an error of roughly 1% for a resolution of 20 points per wavelength and second‐order convergence is achieved for smooth scatterers. Computations of the scattering characteristics for a sinusoidal surface and a random rough surface show similar performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

A numerical scheme is presented for the time‐domain finite‐element modeling of an electrically and magnetically lossy and dispersive medium in the dual‐field domain‐decomposition method. Existing approaches for modeling doubly lossy and dispersive media are extended to the dual‐field case, yielding a general dual‐field domain‐decomposition scheme for modeling large‐scale electromagnetic problems involving such media. A quantitative analysis is performed to estimate the error induced by the modeling of medium dispersion. Copyright © 2012 John Wiley & Sons, Ltd.     

A vectorized multiscale compressed decomposition‐based solver for partial element equivalent circuit method

The high level of integration has made the analysis and design of integrated circuits and packages increasingly challenging. Hence, there exists an urgent need to reduce the computational complexity of existing numerical methods. The integral equation‐based method known as the partial element equivalent circuit (PEEC) method naturally generates an equivalent circuit that can be analyzed in both the time and frequency domains. The enforcement of Kirchhoff laws to the equivalent circuit may easily result into a very large set of equations whose solution can be extremely time‐consuming. In this paper, we propose a vectorized version, over the frequency sweep, of the adaptive cross approximation algorithm. Furthermore, the multiscale block decomposition is applied to the PEEC method, powered by a vectorization strategy and an efficient management of the random access memory. It is found that the proposed use of vectorization and compression techniques in the framework of the multiscale block decomposition results in a significant computational speedup of the frequency‐domain analysis of PEEC models. The efficiency and accuracy of the proposed method are demonstrated through its application to two pertinent problems. Copyright © 2014 John Wiley & Sons, Ltd.     

A modified finite‐difference time‐domain method for analysing field‐to‐transmission line coupling of telecommunication system signals

A modified finite‐difference time‐domain (FDTD) code is presented for the line response characterization of a transmission line illuminated by a Gaussian pulse‐modulated electromagnetic signal. The final expressions are transformed according to the complex‐envelope representation in order to omit the high‐frequency carrier contribution and thus provide an accurate solution of the coupling phenomenon by avoiding the computational burden of the conventional FDTD algorithm. Comparison results between the conventional FDTD method and the modified one are presented, showing the advantages of the novel method. Copyright © 2002 John Wiley & Sons, Ltd.     

Higher‐order finite‐difference schemes with reduced dispersion errors for accurate time‐domain electromagnetic simulations

The potential for developing higher‐order finite‐difference time‐domain (FDTD) schemes with reduced phase errors is investigated in the present paper. Using the classic (2,4) FDTD method as the basis of this study, electromagnetic wave propagation is accurately reproduced in the discretized space by replacing isotropic materials with modified, anisotropic in general, ones. The use of such artificial materials improves the simulation's precision significantly around a specific frequency, yet the overall error remains small at a considerably wide bandwidth; therefore, this algorithm can be useful for wideband problems as well. Additionally, it is shown that an even better single‐frequency performance can be attained, when the modified materials are combined with systematically calculated spatial operators. Pursuing a more wideband enhancement of the (2,4) technique, a version realizing more accurate results at almost all frequencies that can be coupled in a staggered grid is derived. Furthermore, novel spatial operators are introduced, with the distinct feature of using extended stencils in more than one directions. It turns out that when such operators are incorporated, a scheme that combines the aforementioned features can be obtained. The theoretical findings of this investigation are verified in a sequence of numerical tests, involving free‐space and guided‐wave propagation, as well as the determination of a cavity's resonant frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

An accurate time‐domain model of transmission lines with frequency‐dependent parameters

Linear lossy two‐conductor transmission line can be modelled as dynamic two ports in the time domain, via the describing input and transfer impulse responses. This convolution technique is very effective when dealing with networks composed of transmission lines with frequency‐dependent parameters and non‐linear and/or time‐varying circuits. The paper carries out an accurate analysis of this model, in the most general case of lines with frequency‐dependent parameters. For such lines it is not possible to evaluate analytically the impulse responses, nor is it possible to catch them numerically, due to the presence of irregular terms, such as Dirac pulses, terms that numerically behave as Dirac pulses, and functions of the type 1/t^ρ with 0 < ρ <1. A simple method is proposed to evaluate exactly all the irregular terms of the impulse responses: once these irregular parts have been extracted, the regular remainders are easily evaluated numerically. This method is applied to analyse lines with frequency‐dependent parameters of practical interest, such as superconductor transmission lines, power lines above a finite conductivity ground, lines with frequency‐dependent dielectric losses and lines with normal and anomalous skin‐effect. Numerical simulations are carried out for illustration. Copyright © 2000 John Wiley & Sons, Ltd.     

A fast time‐domain EM–TCAD coupled simulation framework via matrix exponential with stiffness reduction

We present a fast time‐domain multiphysics simulation framework that combines full‐wave electromagnetism (EM) and carrier transport in semiconductor devices (technology computer‐aided design (TCAD)) for radio frequency (RF) and mixed‐signal modules. The proposed framework features a division of linear and nonlinear components in the EM–TCAD coupled system. The linear portion is extracted and handled independently with high efficiency by a matrix exponential approach assisted with Krylov subspace method. The nonlinear component is treated by ordinary Newton's method yet with a much sparser Jacobian matrix that leads to substantial speedup in solving the linear system of equations. More convenient error management and adaptive control are also available through the linear and nonlinear decoupling. Furthermore, a new form of system formulation is developed to further enhance the efficiency of the proposed framework by reducing the stiffness of EM–TCAD systems via special equation and variable transforms. Copyright © 2015 John Wiley & Sons, Ltd.     

Extending the enlarged cell and uniformly stable conformal techniques to modeling curved conductors in two‐dimensional high‐order finite‐difference time‐domain algorithms

The critical tool of modeling irregularly shaped perfect conductors is developed for the extended‐stencil high‐order two‐dimensional M24 variant of the finite‐difference time‐domain (FDTD) method. Two standard FDTD conformal approaches are analyzed and successfully extended to work accurately with M24. They both afford higher order convergence with respect to mesh density than a previously developed technique, which better matches M24's characteristics. Both approaches rely on borrowing weighted electromotive forces from nearby extended‐stencil cells to ensure accuracy and numerical stability while the overall algorithm is efficiently operated at the maximum allowable time steps by FDTD and M24 theories. Validation examples demonstrate that M24's amplitude and phase accuracies using coarse numerical meshes were not compromised. Copyright © 2012 John Wiley & Sons, Ltd.     

Transient analysis of printed lines using finite‐difference time‐domain method

Comprehensive studies of ultra‐wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full‐wave 3D finite‐difference time‐domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_r = 1) and with (ϵ_r > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Physical interpretations of the simulation results are discussed in the paper. Copyright © 2012 John Wiley & Sons, Ltd.     

The internal model principle for periodic disturbances with rapidly time‐varying frequencies

In this paper, we study the limitations of scheduling an internal model to reject disturbances with a time‐varying frequency. Hence, any adaptive method that uses scheduling and frequency estimation is also limited in the same manner. The limitations of scheduling are to investigate by posing and solving the problem of rejecting periodic disturbances from a multichannel system when the frequencies of the periodic disturbances are changing rapidly in time by designing an scheduled controller that satisfies the internal model principle. The periodic disturbances are modeled by a sum of sinusoids and the frequencies of the disturbances are used for scheduling the controller. It is shown that a controller that regulates input additive disturbances may not regulate the same disturbances added to the output of the system. This is in contrast to the classical case where the frequency of the disturbances is constant. Copyright © 2011 John Wiley & Sons, Ltd.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.     

Fast and accurate analysis of one‐dimensional arrays of dynamic PWL cells

This paper describes a new method for the time‐domain analysis of one‐dimensional arrays of dynamic piecewise linear cells. The method exploits the local connectivity, typical of cellular arrays, and the piecewise linear behaviour of the v–i characteristic of the non‐linear elements to obtain a piecewise analytical expression of the solution. Examples demonstrate the accuracy and the efficiency, in terms of CPU‐time, of the proposed method with respect to standard simulation tools as SPICE and the numerical integration of a system of ordinary differential equations. Copyright © 2001 John Wiley & Sons, Ltd.     

Convergence analysis of generalized conjugate direction method to solve general coupled Sylvester discrete‐time periodic matrix equations

The discrete‐time periodic matrix equations have been extensively applied as a main tool of analysis and design for periodic systems. This study is intended to provide a generalization of conjugate direction method for solving the general coupled Sylvester discrete‐time periodic matrix equations The convergence theorem guarantees that the generalized conjugate direction method can compute the solutions of the general coupled Sylvester discrete‐time periodic matrix equations after a finite number of iterations in the absence of round‐off errors. Finally, numerical results are given to exhibit the accuracy and efficiency of the generalized conjugate direction method. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer design for neutral‐type neural networks with discrete and distributed time‐varying delays

This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method.     

Simple and accurate approaches to implement the complex trans‐conductance suited for time‐domain simulators for small‐signal and large‐signal table‐based models

This paper focuses on the implementation of table‐based models of high‐frequency transistors for time‐domain simulators at microwave and mm‐wave frequencies. In this frequency range, the channel is not capable of responding to the excitation instantaneously therefore, a delay‐time exists between the channel response and the channel excitation. This delay is represented by a complex trans‐conductance in terms of circuit elements. The high‐frequency models of transistors are required to have the implementation of complex trans‐conductance, where the complex part accounts mathematically for the delay‐time between the channel response and the channel excitation. This paper presents simple and accurate approaches to incorporate the complex trans‐conductance in both small‐signal and large‐signal table‐based models for time‐domain simulators (MOS‐AK International Meeting. Eindhoven, Netherlands, April 2008). Implementation approach for each model, small‐signal and large‐signal, is presented in separated sections. In the first step, the delay is realized by the introduction of an ideal transmission line between the channel excitation and the channel response. As transmission lines are not generally suitable for time‐domain simulations, a lumped element equivalent network is introduced in the second step. The latter approach is fully compatible with time‐domain simulators but frequency limitation, determined by the delay‐time value itself, is introduced. Then the implementation of the complex trans‐conductance in large‐signal model is introduced. In terms of large‐signal behavior, delay‐time is important to achieve a non‐quasi static model. Yet again there is limitation in terms of the frequency range that is determined by the delay value itself. The methodology is illustrated on the small‐signal and the large‐signal equivalent circuit of a Multi‐Fin MOSFET transistor. Simulations are carried out by Cadence Spectre and Agilent ADS simulators, and comparisons are carried out between the simulation results and the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Almost invariant manifold approach for adaptive estimation of periodic and aperiodic unknown time‐varying parameters

This paper provides a novel identification technique for the estimation of time‐varying parameters in a class of nonlinear dynamical systems. The concept of almost invariant manifold is used to find an implicit mapping from known variables of the system to the unknown variables. A parameter estimation update law is generated from the proposed mapping. The exponential convergence of parameter estimation error to a small neighbourhood of the origin is achieved. The algorithm is extended to estimate the uncertain periodic parameters. An upper bound estimation of the unknown periodic parameters and their time derivatives are obtained. Unlike most periodic time‐varying parameter estimation techniques, only the knowledge of the number of distinctive frequencies is assumed. The effectiveness of the proposed method is illustrated with two simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time‐harmonic EM field problems

Based on message passing interface (MPI) distributed‐memory network, we propose a parallel realization of algebraic domain decomposition method to solve the large sparse linear systems, which were derived from the vector finite element method (FEM) for three‐dimensional electromagnetic field problems. The proposed method segments the problem into several smaller sub‐problems, solves each sub‐problem in each node (i.e. computer) by the direct method, exchanges related data between nodes with MPI cluster network, and then reassembles the sub‐problem solutions together to get the global result. Multifrontal method is applied to solve intermediate equations associated with each sub‐problem and conjugate gradient methods are used to solve the reduced interface system. The simulation results demonstrate that the proposed parallel computing can save much more memory and CPU time than sequential computing. Furthermore, it can solve larger system in reasonable time and get excellent performance vs price ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

The mortar edge element method on non‐matching grids for eddy current calculations in moving structures

The subject presented in this paper concerns the approximation of the eddy current problem in non‐stationary geometries with sliding interfaces. The physical system is supposed to be composed of two solid parts: a fixed one (stator) and a moving one (rotor) which slides in contact with the stator. We consider a two‐dimensional mathematical model based on the transverse electric formulation of the eddy currents problem in the time domain and the primary unknown is the electric field vector. The first‐order approximation of the problem that we propose here is based on the mortar element method combined with the edge element discretization in space and an implicit Euler scheme in time. Numerical results illustrate the accuracy of the method and allow to understand the influence of the rotor movement on the currents distribution. Copyright © 2001 John Wiley & Sons, Ltd.     

Sliding mode control of switched hybrid systems with time‐varying delay

This paper is concerned with the sliding mode control of a continuous‐time switched system with time‐varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced‐order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed‐loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory. Copyright © 2008 John Wiley & Sons, Ltd.     

2‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

In this article, we propose ²‐based finite element (FE) solver for transient thermal analysis of high‐performance integrated circuits (ICs). ²‐matrix is a special subclass of hierarchical matrix or ‐matrix, which was shown to provide a data‐sparse way to approximate the matrices and their inverses with almost linear space and time complexities. In this work, we show that ²‐based mathematical framework can also be applied to FE‐based transient analysis of thermal parabolic partial differential equations. We show how the thermal matrix can be approximated by ²‐representations with controlled error. Then, we demonstrate that both storage and time complexities of the new solver are bounded by , where N is the matrix size. The method can be applied to any thermal structures for both steady and transient analysis. The numerical results from 3D ICs demonstrate the linear scalability of the proposed method in terms of both memory footprint and CPU time. The comparison with existing product‐quality LU solvers, CSPARSE and UMFPACK, on a number of 3D IC thermal matrices, shows that the new method is much more memory efficient than these methods, which however prevents the demonstration of the potential speedup of the proposed method over those methods. Copyright © 2014 John Wiley & Sons, Ltd.