Modeling of ultra‐wideband indoor channels with the modified leapfrog ADI‐FDTD method

Full‐wave time‐domain electromagnetic methods are usually effective in rigorously modeling and evaluating ultra‐wideband (UWB) wireless channels. However, their computational expenditures are expensive, when they are used to deal with electrically large‐size problems consisting of fine structures. In order to reduce computational time, the unconditionally stable leapfrog alternating‐direction implicit finite‐difference time‐domain (leapfrog ADI‐FDTD) method has been proposed recently. In this paper, the leapfrog ADI‐FDTD algorithm is developed for simulating lossy objects, such as office walls, floors, and ceilings, for UWB communication channel characterization. It leads to effective UWB channel characterization with power‐decay time constant, path loss exponent, and probability distribution of power gain. In comparison with the conventional FDTD, the proposed method can achieve 60% saving in computational time while retaining good accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Electromagnetic radiation from vertical dipole antennas near air–lossy soil interface—a finite‐difference time‐domain simulation

Radiation from vertical dipole antennas, which are located over or under the surface of lossy earth, is analysed by the finite‐difference time‐domain (FDTD) method in cylindrical coordinates. A novel generalized perfectly matched layer (PML) has been developed and used for the truncation of the lossy soil. In order to decrease the memory requirements and for having an accurate modelling, an efficient ‘non‐uniform’ mesh generation scheme is used. The excitation is considered in the form of sine carrier modulated by Gaussian pulse (SCMGP) and in each time step, computation is limited to that part of the mesh where the radiated pulse is passing (computational window). This could considerably reduce the required CPU time. In this manner, large‐scale problems can be solved and the values of radiated field at far distances (up to 500λ₀ in this work) can be obtained directly by the FDTD method. The frequency‐domain results are calculated from the obtained time‐domain results by taking the Fourier transform. The spatial distributions of the amplitude and phase of radiated field are shown in illustrations for different types of soil and different positions of antenna. The influence of the lossy soil on dipole's admittance is also shown. Copyright © 2005 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.     

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

A time‐domain method for calculating the band structure of one‐dimensional periodic structures is proposed. During the time‐stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix‐exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix–vector multiplication involved in each time‐step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finite‐difference time‐domain (FDTD) method. The time‐step with which the method runs stably can be much larger than the Courant–Friedrichs–Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large‐scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix‐pruning operation can be very effectively performed. In the numerical experiments for large‐scale quasi‐periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite‐difference time‐domain analysis of radiation characteristics of monopoles on space probes

A general numerical solution based on finite‐difference time‐domain (FDTD) is presented to calculate the radiation characteristics of wire antennas on space probes. The method is versatile and can treat conductor loss, arbitrary‐shaped probes, and wires as well as inhomogenities. Numerical results are obtained and compared with those for a few specific cases available in the literature. Additionally, laboratory models of the antennas have been built and their properties have been measured for comparison with computed results. Copyright © 2008 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.     

PML absorbing boundary condition for the integral‐based high‐order FV24 FDTD algorithm

An integral equations‐based perfectly matched layers (PML) implementation is presented for the highly phase‐coherent FV24 finite‐difference time‐domain (FDTD) algorithm. The implementation allows including field values off the grid axes in the split‐field PML formulation conserving in the process the continuity and phase coherency of the FV24 algorithm when modeling absorbing boundary conditions (ABCs). It also eliminates the need for cumbersome subgridded low‐order FDTD subregions that until now were required to model PML ABCs within integral‐based high‐order FDTD simulations. The developed approach was numerically tested and found to match the PML behavior of the standard FDTD method at normal wave incidence on ABC boundaries and exceeds it at highly oblique wave incidence. This development serves to improve the capability and practicality of the computationally efficient FV24 algorithm when modeling electrically large structures in 3‐D space. Copyright © 2010 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.     

Modelling of lossy curved surfaces in the 3‐D frequency‐domain finite‐difference methods

A conformal first‐order or Leontovic surface‐impedance boundary condition (SIBC) for the modelling of fully three‐dimensional (3‐D) lossy curved surfaces in a Cartesian grid is presented for the frequency‐domain finite‐difference (FD) methods. The impedance boundary condition is applied to auxiliary tangential electric and magnetic field components defined at the curved surface. The auxiliary components are subsequently eliminated from the formulation resulting in a modification of the local permeability value at boundary cells, allowing the curved 3‐D surface to be described in terms of Cartesian grid components. The proposed formulation can be applied to model skin‐effect loss in time‐harmonic driven problems. In addition, the impedance matrix can be used as a post‐processor for the eigenmode solver to calculate the wall loss. The validity of the proposed model is evaluated by investigating the quality factors of cylindrical and spherical cavity resonators. The results are compared with analytic solutions and numerical reference data calculated with the commercial software package CST Microwave Studio™ (MWS). The convergence rate of the results is shown to be of second‐order for smooth curved metal surfaces. The overall accuracy of the approach is comparable to that of CST MWS™. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance of proposed thin‐wire model in finite difference time domain method

Thin‐wire approximation in the finite difference time domain (FDTD) method is important in saving computer resources and truncating central processing unit (CPU) time. Previously, thin wires were mainly realized using the true thin wire (TTW) model, in which electric field components along the wire axis are set at zero, and three methods, in which electric field components along the wire axis are also set at zero and the medium around thin wires is replaced depending on wire radius, are hereafter called the RM model. The former is the most conventional and widely used method; however, its resultant radius is 0.23Δs, supposing that the space under consideration is divided by cubic cells with a Δs of the side length of FDTD cells. The first method of the RM model can realize thin wires having a radius of about 0.15Δs under the conditions we used, in which the time interval is set at a value which is slightly less than Δt_c, e.g. 0.9999t_c, where Δt_c is defined by the Courant condition; in the case of a thin wire having a radius less than 0.15Δs, the FDTD computation suffers from numerical instability. The second method can realize a thin wire having a radius of about 10⁻⁴Δs. We need some changes in the numerical electromagnetic analysis program based on the FDTD method to employ these models. The third of the RM model, which has already been proposed by the author and in which the relative permittivity and relative permeability of four FDTD cells closest to a thin wire are replaced according to the radius of the thin wire and Δs, could realize thin wires having a radius of about 10⁻⁶Δs without changing the program and numerical instability. In this paper, the third model is extensively investigated and it is demonstrated that we can deal with a thin wire with a radius of about 10⁻⁹Δs without numerical instability. The maximum difference in the evaluation of the surge impedance of an open‐ended horizontal wire located 5 m above a perfectly conducting ground is less than 5%. We can easily use the third model even though the program, which is available, has no the specific function of thin‐wire approximation. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Using WCS‐FDTD method to simulate various cylindrical metallic enclosures

The weakly conditionally stable (WCS) finite‐difference time‐domain (WCS‐FDTD) method in the cylindrical coordinate system is employed to compute the electromagnetic coupling and shielding of various cylindrical enclosures. In the WCS‐FDTD method, a larger time‐step size than that allowed by the Courant–Friedrich–Levy stability condition limitation can be set because the algorithm of this method is WCS. Consequently, an increase in computational efforts caused by fine cells due to thin sots can be prevented. The results from the WCS‐FDTD method agree well with the results from the conventional FDTD method, and the required CPU time for the WCS‐FDTD method is much shorter than that for the FDTD method. Careful investigation of different aspects of the shielding properties of the cylindrical enclosures is performed, and the shielding performance of the cylindrical enclosure and rectangular enclosure is compared. The result obtained in this paper can be used to design a practical cylindrical shielding enclosure. Copyright © 2010 John Wiley & Sons, Ltd.     

Time‐domain sensitivity analysis of planar structures using first‐order one‐way wave‐equation boundaries

An efficient adjoint variable method technique is developed for time‐domain sensitivity analysis of planar structures with transmission‐line modeling complemented by a first‐order one‐way wave‐equation absorbing boundaries. A backward‐running adjoint simulation is derived and solved. The validity of the technique is illustrated through three microstrip circuits. The examples demonstrate the efficiency and accuracy of the technique in comparison with the classical finite‐difference approaches to the estimation of the response sensitivities. Copyright © 2007 John Wiley & Sons, Ltd.     

Investigation of numerical time‐integrations of Maxwell's equations using the staggered grid spatial discretization

The Yee‐method is a simple and elegant way of solving the time‐dependent Maxwell's equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time‐steps. This is why, during the last decade, the main goal was to construct such methods that are unconditionally stable. This means that the time‐step can be chosen based only on accuracy instead of stability considerations. In this paper we give a uniform treatment of methods that use the same spatial staggered grid approximation as the classical Yee‐method. Three other numerical methods are discussed: the Namiki–Zheng–Chen–Zhang alternating direction implicit method (NZCZ), the Kole–Figge‐de Raedt method (KFR) and a Krylov‐space method. All methods are discussed with non‐homogeneous material parameters. We show how the existing finite difference numerical methods are based on the approximation of a matrix exponential. With this formulation we prove the unconditional stability of the NZCZ method without any computer algebraic tool. Moreover, we accelerate the Krylov‐space method with a skew‐symmetric formulation of the semi‐discretized equations. Our main goal is to compare the methods from the point of view of the computational speed. This question is investigated in ID numerical tests. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient parallel PML algorithms for truncating finite difference time domain simulations

In this paper, the parallel implementation of the stretched coordinate perfectly matched layer (SC-PML) and the wave equation PML (WE-PML) formulations is presented for truncating three-dimensional (3-D) finite difference time domain (FDTD) grids. In the proposed parallel algorithms, the FDTD computational domain is divided into contiguous non-overlapping subdomains using two-dimensional topology and the interprocessor communications between the neighboring subdomains are carried out by using the message passing interface (MPI) system. The performance of the proposed parallel algorithms has been studied by using a point source radiating in 3-D domains and performed on a network of PCs interconnected with Ethernet. It has been observed that the WE-PML parallel algorithm is approximately 2.3 faster than the SC-PML parallel algorithm.     

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.