A new parallelization strategy for solving time‐dependent 3D Maxwell equations using a high‐order accurate compact implicit scheme

With progress in computer technology there has been renewed interest in a time‐dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second‐order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high‐order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd‐order accurate explicit scheme for approximation of spatial derivatives with the 4th‐order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl‐based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three‐dimensional time‐dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Global modeling of nonlinear circuits using the finite‐difference Laguerre time‐domain/alternative direction implicit finite‐difference time‐domain method with stability investigation

This paper describes a new unconditionally stable numerical method for the full‐wave physical modeling of semiconductor devices by a combination of the finite‐difference Laguerre time‐domain (FDLTD) and alternative direction implicit finite‐difference time‐domain (ADI‐FDTD) approaches. The unconditionally stable method by using FDLTD scheme for the electromagnetic model and semi‐implicit ADI‐FDTD approach for the active model leads to a significant decrease in the full‐wave simulation time. Numerical simulations of an example transistor and a power amplifier show the efficiency of presented method for the full‐wave simulation of mm‐wave active circuits. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive stabilization of neutral systems with nonlinear perturbations and mixed time‐varying delays

This paper addresses the stabilization problem of neutral systems. The neutral systems assumed to be subjected to nonlinear perturbations and mixed time‐varying delays. Specifically, the adaptive control method is used to stabilize the unknown neutral systems. If the system states and the delayed states with its derivatives are available for measurement, a new and less conservative adaptive control algorithm is proposed, and sufficient conditions for the existence of the adaptive control are derived based on Lyapunov's stability theory. The main idea is to make all the stability conditions of the system depend on desired arbitrary matrices, not on the given system matrices. This is accomplished by the adaptation process. Illustrative examples with numerical simulations are studied. The simulation results show the effectiveness of the proposed design methods. Copyright © 2015 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.     

State‐space equations of regular and strictly topologically degenerate linear lumped time‐invariant networks: the multiport method

A new complete approach to the multiport formulation of the state‐space equations of uniquely solvable regular or strictly topologically degenerate linear lumped time‐invariant networks is presented. It is based on a Gedankenexperiment during which the topological structure of the original network is manipulated in various ways. The final method requires one to calculate the describing matrices of three homogeneous multiports (i.e. a capacitive, an inductive and a resistive one), which are obtained from the network of interest in a very simple manner. As a by‐product, the equivalent partitioned network is also derived. As an example of application, the state‐space equations of a fourth‐order strictly topologically degenerate network are provided. Copyright © 2001 John Wiley & Sons. Ltd.     

A three‐dimensional mesh refinement algorithm with low boundary reflections for the finite‐difference time‐domain simulation of metallic structures

We present a method for including areas of high grid density into a general grid for the finite‐difference time‐domain method in three dimensions. Reflections occurring at the boundaries separating domains of different grid size are reduced significantly by introducing appropriate interpolation methods for missing boundary points. Several levels of refinement can be included into one calculation using a hierarchical refinement architecture. The algorithm is implemented with an auxiliary differential equation technique that allows for the simulation of metallic structures. We illustrate the performance of the algorithm through the simulation of metal nano‐particles included in a coarser grid and by investigating gold optical antennas. Copyright © 2009 John Wiley & Sons, Ltd.     

A high‐order discontinuous Galerkin method with time‐accurate local time stepping for the Maxwell equations

We present an explicit numerical method to solve the time‐dependent Maxwell equations with arbitrary high order of accuracy in space and time on three‐dimensional unstructured tetrahedral meshes. The method is based on the discontinuous Galerkin finite element approach, which allows for discontinuities at grid cell interfaces. The computation of the flux between the grid cells is based on the solution of generalized Riemann problems, which provides simultaneously a high‐order accurate approximation in space and time. Within our approach, we expand the solution in a Taylor series in time, where subsequently the Cauchy–Kovalevskaya procedure is used to replace the time derivatives in this series by space derivatives. The numerical solution can thus be advanced in time in one single step with high order and does not need any intermediate stages, as needed, e.g. in classical Runge–Kutta‐type schemes. This locality in space and time allows the introduction of time‐accurate local time stepping (LTS) for unsteady wave propagation. Each grid cell is updated with its individual and optimal time step, as given by the local Courant stability criterion. On the basis of a numerical convergence study we show that the proposed LTS scheme provides high order of accuracy in space and time on unstructured tetrahedral meshes. The application to a well‐acknowledged test case and comparisons with analytical reference solutions confirm the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamics of charge‐pump phase‐locked loops

Certain problems in the existing treatment of the stability of charge‐pump phase‐locked loops are identified and addressed in this work. New results concerning the instability, stability, and asymptotic stability of charge‐pump phase‐locked loops are obtained by means of Lyapunov's direct and indirect methods. Closer consideration of the local dynamics provides further insight into the system's patterns of behavior. In particular, the influence of circuit parameters on the nature of the steady‐state orbits is investigated. Copyright © 2012 John Wiley & Sons, Ltd.     

Approximation of the inverse of the Hodge matrix via sparsity pattern

The solution of electromagnetic wave propagation problems in time domain using an explicit method requires the inversion of Hodge matrices. This paper proposes an approximation to obtain a sparse inverse via the sparsity pattern of the original matrix. It is also shown the application of the algorithm Cuthill–McKee on Hodge matrices in order to reduce their bandwidth and thus speed up the method of recursive sparsification. Copyright © 2014 John Wiley & Sons, Ltd.     

Design and analysis of low‐speed,high‐torque permanent magnet motors

This paper presents design and analysis of low‐speed, high‐torque permanent magnet motors. The motor has 16‐pole, 18‐coil construction, and a unique winding arrangement to produce high torque. The simplified torque analysis is proposed considering the line of magnetic induction distribution in the motor. The validity of the proposed analysis has been proved by both linear and nonlinear FEM analyses. The 500‐Nm, 200‐rpm test motor has been designed and constructed and the motor shows the expected characteristics. © 2000 Scripta Technica, Electr Eng Jpn, 132(3): 48–56, 2000     

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.     

Stability analysis for the AIBO‐FDTD method

The stability of the implicit finite‐difference time‐domain (FDTD) method named alternating implicit block overlapped (AIBO) FDTD is presented in this paper. Based on separation of variables method, the spectral radius of the growth matrix for AIBO‐FDTD is obtained. Analytical results show that the AIBO‐FDTDs both in one‐dimensional and two‐dimensional cases are unconditionally stable. But it is conditionally stable in 3D case, like the conventional FDTD. Numerical results are also presented to demonstrate its effectiveness for parallel processing. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiscalet basis in Galerkin's method for solving three‐dimensional electromagnetic integral equations

Multiscalets in the multiwavelet family are used as the basis and testing functions in Galerkin's method. Since the multiscalets are orthogonal to their translations under the Sobolev inner product, the resulting Galerkin's method behaves like a collocation method but possesses the ability of derivative tracking for unknown functions in solving integral equations. The former makes the method simple in implementation and the latter allows to use coarse meshes in discretization. These robust features have been demonstrated in solving two‐dimensional (2D) electromagnetic (EM) problems, but have not been exploited in three‐dimensional (3D) scenarios. For 3D problems, the unknown functions in the integral equations are dependent on two coordinate variables. In order to preserve the use of coarse meshes for 3D cases, we realize the omnidirectional derivative tracking by tracking the directional derivatives along two orthogonal directions, or equivalently tracking the gradient. This process yields a nonsquare matrix equation and we use the least‐squares method (LSM) to solve it. Numerical examples show that the multiscalet‐based Galerkin's method is also robust in solving for 3D EM integral equations with a minor cost increase from LSM. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive B‐spline neural network‐based vector control for a grid side converter in wind turbine‐DFIG systems

This paper presents a novel control system design for the grid‐side converter of doubly fed induction generator wind power generation systems. The control method proposed in this work is a vector control based on adaptive B‐spline neural network by using a simple fixed‐gain stabilizing control topology. The adaptive control is designed both for inner current loops and an outer DC‐link voltage loop of the grid side converter control system. To guarantee the control stability, the weights updating rule for the B‐spline neural network is synthesized by utilizing Lyapunov's direct method. To verify the effectiveness of the proposed control system, extensive simulations are performed using MATLAB/Simulink. Based on the simulation results, it is concluded that the proposed controller has improved performance compared to an optimum proportional integral control system. It is also relatively robust against external disturbances and variations of the control parameters. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

An efficient approach for computing non‐Gaussian ARMA model coefficients using Pisarenko's method

This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the system output. The observed signal may be corrupted by additive coloured Gaussian noise. The system is driven by a zero‐mean independent and identically distributed (i.i.d.) non‐Gaussian sequence. The input is not observed. The unknown model coefficients are obtained using eigenvalue–eigenvector decomposition. The derivation of this procedure is an extension of Pisarenko harmonic autocorrelation‐based (PHA) method to third order statistics. It will be shown that the desired ARMA coefficients vector corresponds to the eigenvector associated with the minimum eigenvalue of a data covariance matrix of TOCs. The proposed method is also compared with well‐known algorithms as well as with the PHA method. Copyright © 2005 John Wiley & Sons, Ltd.     

Wide‐band modelling of CMOS interconnections and voiding damages with the lumped element LE‐FDTD method

This paper illustrates the application of a lumped element‐finite difference time domain (LE‐FDTD) simulator to the wide‐band modelling of CMOS interconnections. To achieve very accurate results the short‐open calibration (SOC) technique has been adopted. Specific parameters of a CMOS interconnection laterally screened by a stack of metal vias have been extracted in the two cases of an unperturbed and a purposely damaged metal line. The behaviour of void‐like defects in the metal line has been also studied using the fully three‐dimensional capabilities of the simulator. It has been demonstrated that, at least in the simulated cases, only the specific resistance is affected by damaging. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison of several discretization methods of the Steklov–Poincaré operator

In this paper, we present three methods to discretize the Steklov–Poincaré operator. Two of these methods are already well known and commonly used and the third one is new. These methods are based either on the ballooning technique or on the integral theory or on the Calderon equations and we recall the principles of the discretization for each method. Then, we implement these discretization procedures in a code which treats the three‐dimensional magnetostatic problem with a mixed and hybrid finite element method. The exterior domain is treated with the Steklov–Poincaré operator discretized using the three procedures. A comparison in terms of precision, performance and ease of implementation is given. Copyright © 2006 John Wiley & Sons, Ltd.