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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

This paper aims to explore the limitations of the conformal finite difference time-domain method (C-FDTD or Dey–Mittra) when modeling perfect electric conducting (PEC) and lossless dielectric curved surfaces in coarse meshes. The C-FDTD is a widely known approach to reduce error of curved surfaces in the FDTD method. However, its performance limitations are not broadly described in the literature, which are explored as a novelty in this paper.

This paper explores the C-FDTD method applied on field scattering simulations of two curved surfaces, a dielectric and a PEC sphere, through the frequency range from 0.8 to 10 GHz. For each sphere, the mesh was progressively impoverished to evaluate the accuracy drop and performance limitations of the C-FDTD with the mesh impoverishment, along with the wideband frequency range described.

This paper shows and quantifies the C-FDTD method’s accuracy drops as the mesh is impoverished, reducing C-FDTD’s performance. It is also shown how the performance drops differently according to the frequency of interest.

With this study, coarse meshes, with smaller execution time and reduced memory usage, can be further explored reliably accounting the desired accuracy, enabling a better trade-off between accuracy and computational effort.

This paper quantifies the limitations of the C-FDTD in coarse meshes in a wideband manner, which brings a broader and newer insight upon C-FDTD’s limitations in coarse meshes or relatively small objects in electromagnetic simulation.

The purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations.

In this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed.

It is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation.

The stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit.

Based on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function.

The proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

The purpose of the paper is to introduce a perfectly matched layer (PML) absorber, based on Berenger's split field PML, to the recently proposed low-dispersion precise integration time domain method using a fourth-order accurate finite difference scheme (PITD(4)).

The validity and effectiveness of the PITD(4) method with the inclusion of the PML is investigated through a two-dimensional (2-D) point source radiating example.

Numerical results indicate that the larger time steps remain unchanged in the procedure of the PITD(4) method with the PML, and meanwhile, the PITD(4) method employing the PML is of the same absorbability as that of the finite-difference time-domain (FDTD) method with the PML. In addition, it is also demonstrated that the later time reflection error of the PITD(4) method employing the PML is much lower than that of the FDTD method with the PML.

An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations.

Random media uncertainties exhibit a significant impact on the properties of electromagnetic fields that usually deterministic models tend to neglect. As a result, these models fail to quantify the variation in the calculated electromagnetic fields, leading to inaccurate outcomes. This paper aims to introduce an unconditionally stable finite-difference time-domain (FDTD) method for assessing two-dimensional random media uncertainties in one simulation.

The proposed technique is an extension of the stochastic FDTD (S-FDTD) scheme, which approximates the variance of a given field component using the Delta method. Specifically in this paper, the Delta method is applied to the locally one-dimensional (LOD) FDTD scheme (hence named S-LOD-FDTD), to achieve unconditional stability. The validity of this algorithm is tested by solving two-dimensional random media problems and comparing the results with other methods, such as the Monte-Carlo (MC) and the S-FDTD techniques.

This paper provides numerical results that prove the unconditional stability of the S-LOD-FDTD technique. Also, the comparison with the MC and the S-FDTD methods shows that reliable outcomes can be extracted even with larger time steps, thus making this technique more efficient than the other two aforementioned schemes.

The S-LOD-FDTD method requires the proper quantification of various correlation coefficients between the calculated fields and the electrical parameters, to achieve reliable results. This cannot be known beforehand and the only known way to calculate them is to run a fraction of MC simulations.

This paper introduces a new unconditional stable technique for measuring material uncertainties in one realization.

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures.

The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition.

It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results.

An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations.

Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed.

The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation.

The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

The computational accuracy and performance of finite-difference time-domain (FDTD) methods are affected by the implementation of approximating derivative formulae in diverse ways. This study aims to focus on FDTD models featuring material dispersion with negligible losses and investigates two specific aspects that, until today, are usually examined in the context of non-dispersive media only. These aspects pertain to certain abnormal characteristics of coarsely resolved electromagnetic waves and the selection of the proper time-step size, in the case of a high-order discretization scheme.

Considering a Lorentz medium with negligible losses, the propagation characteristics of coarsely resolved waves is examined first, by investigating thoroughly the numerical dispersion relation of a typical discretization scheme. The second part of the study is related to the unbalanced space-time errors in FDTD schemes with dissimilar space-time approximation orders. The authors propose a remedy via the suitable choice of the time-step size, based on the single-frequency minimization of an error expression extracted, again, from the scheme’s numerical dispersion formula.

Unlike wave propagation in free space, there exist two parts of the frequency spectrum where waves in a Lorentz medium experience non-physical attenuation and display non-changing propagation constants, due to coarse discretization. The authors also show that an optimum time-step size can be determined, in the case of the (2,4) FDTD scheme, which minimizes the selected error formula at a specific frequency point, promoting more efficient implementations.

Unique characteristics displayed by discretized waves, which have been known for non-dispersive media, are examined and verified for the first time in the case of dispersive materials, thus completing the comprehension of the space-time discretization impact on simulated quantities. In addition, the closed-form formula of the optimum time-step enables the efficient implementation of the (2,4) FDTD method, minimizing the detrimental influence of the low-order temporal integration.

The purpose of this paper is to present efficient and stable generalized auxiliary differential equation finite difference time domain (G-ADE-FDTD) implementation of graphene dispersion.

A generalized dispersive model is used for describing the graphene’s intraband and interband conductivities in the terahertz and infrared frequencies. In addition, the von Neumann method combined with the Routh-Hurwitz criterion are used for studying the stability of the given implementation.

The presented G-ADE-FDTD implementation allows modeling graphene’s dispersion using the minimal number of additional auxiliary variables, which will reduce both the CPU time and memory storage requirements. In addition, the stability of the implementation retains the standard non-dispersive Courant–Friedrichs–Lewy (CFL) constraint.

The given implementation is conveniently applicable for most commonly used dispersive models, such as Debye, Lorentz, complex-conjugate pole residue, etc.

The presented G-ADE-FDTD implementation not only unifies the implementation of both graphene’s intraband and interband conductivities, with the minimal computational requirements but also retains the standard non-dispersive CFL time step stability constraint.