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The paper seeks to investigate the precise time‐domain modelling and broadband performance optimisation of 3D EMC structures formed by composite left‐handed metamaterials.

A frequency‐dependent alternating‐direction implicit finite‐difference time‐domain method is introduced. Developing a class of multi‐directional curvilinear schemes for double‐negative media, the unconditionally stable algorithm forms robust lattice tessellations and provides advanced models complicated media interfaces. Moreover, the erroneous refractions at the metamaterial boundaries are systematically analysed through dynamic stencil configurations and powerful perfectly matched layer absorbers.

The paper finds that the proposed technique leads to convergent discretisations that resolve all propagation bandwidths and enhances the design of promising periodical devices loaded by substrates of thin wires and split‐ring resonators. Furthermore, its versatile character subdues dispersion deficiencies far beyond the usual stability criteria. Numerical validation, addressing various up‐to‐date EMC devices like coupled antennas, waveguides, high‐pass filters and absorber linings in test facilities, confirms the merits of the algorithm.

The novel methodology offers an advanced nodal control process which drastically suppresses the serious dispersion errors of existing approaches as time‐step exceeds the Courant limit. The resulting grids can support coarse resolutions, while the general curvilinear framework, along with the ADI rationale, allows the accurate approximation of demanding permittivity and permeability constitutive profiles. Hence, high accuracy and confined computational overhead are achieved without the need of laborious assumptions.

To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions.

The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions.

Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic.

Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist.

Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time.

Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

The paper introduces and illustrates the use of numerical models for the simulation of electromagnetic and thermal processes in an absorbing ceramic layer (susceptor) of a new millimeter-wave (MMW) heat exchanger. The purpose of this study is to better understand interaction between the MMW field and the susceptor, choose the composition of the ceramic material and help design the physical prototype of the device.

A simplified version of the heat exchanger comprises a rectangular block of an aluminum nitride (AlN) doped with molybdenum (Mo) that is backed by a thin metal plate and irradiated by a plane MMW. The coupled electromagnetic-thermal problem is solved by the finite-difference time-domain (FDTD) technique implemented in QuickWave. The FDTD model is verified by solving the related electromagnetic problem by the finite element simulator COMSOL Multiphysics. The computation of dissipated power and temperature is based on experimental data on temperature-dependent dielectric constant, loss factor, specific heat and thermal conductivity of the AlN:Mo composite. The non-uniformity of patterns of dissipated power and temperature is quantified via standard-deviation-based metrics.

It is shown that with the power density of the plane wave on the block’s front face of 1.0 W/mm², at 95 GHz, 10 × 10 × 10-mm blocks with Mo = 0.25 – 4% can be heated up to 1,000 °C for 60-100 s depending on Mo content. The uniformity of the temperature field is exceptionally high – in the course of the heating, temperature is evenly distributed through the entire volume and, in particular, on the back surface of the block. The composite producing the highest level of total dissipated power is found to have Mo concentration of approximately 3%.

In the electromagnetic model, the heating of the AlN:Mo samples is characterized by the volumetric patterns of density of dissipated power for the dielectric constant and the loss factor corresponding to different temperatures of the process. The coupled model is run as an iterative procedure in which electromagnetic and thermal material parameters are upgraded in every cell after each heating time step; the process is then represented by a series of thermal patterns showing time evolution of the temperature field.

Determination of practical dimensions of the MMW heat exchanger and identification of material composition of the susceptor that make operations of the device energy efficient in the required temperature regime require and expensive experimentation. Measurement of heat distribution on the ceramic-metal interface is a practically challenging task. The reported model is meant to be a tool assisting in development of the concept and supporting system design of the new MMW heat exchanger.

While exploitation of a finite element model (e.g. in COMSOL Multiphysics environment) of the scenario in question would require excessive computational resources, the reported FDTD model shows operational capabilities of solving the coupled problem in the temperature range from 20°C to 1,000°C within a few hours on a Windows 10 workstation. The model is open for further development to serve in the ongoing support of the system design aiming to ease the related experimental studies.

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 purpose of this work is to develop a computational paradigm for performance analysis of low-frequency electromagnetic devices containing both magnetic metamaterials (MTMs) and natural media.

A time domain finite element method (TDFEM) is proposed. The electromagnetic properties of the MTMs are modeled by a nonstandard Lorentz model. The time domain governing equation is derived by converting the one from the frequency domain into the time domain based on the Laplace transform and convolution. The backward difference is used for the temporal discretization. An auxiliary variable is introduced to derive the recursive formula.

The numerical results show good agreements between the time domain solutions and the frequency domain solutions. The error convergence trajectory of the proposed TDFEM conforms to the first-order accuracy.

To the best knowledge of the authors, the presented work is the first one focusing on TDFEMs for low-frequency near fields computations of MTMs. Consequently, the proposed TDFEM greatly benefits the future explorations and performance evaluations of MTM-based near field devices and systems in low-frequency electrical and electronic engineering.

A general time domain finite element formulation and several efficient numerical techniques are combined to form a new method of analysis for the solution of three‐dimensional soil‐structure interaction problems in the time domain. For elastic systems the method is a very cost effective alternative to the frequency domain approach. However, the major advantage of the new method is its ability to be extended to non‐linear behaviour such as separation of foundation and soil or non‐linear material. The general equations of motion for the linear cases are expressed in terms of the relative displacements of the soil‐structure system with respect to the displacements of the buried part of the structure (volume methods). This formulation allows the load vector to be an exclusive function of the free field accelerations at the foundation level. The non‐linear case requires that the equation of motion be established in terms of the total interaction displacements. The soil is modelled with three‐dimensional solid elements in the near field and axisymmetric elements in the far field. Coupling between the two systems is enforced by expanding the displacements of the solid elements in terms of the axisymmetric ones. Reduction in the number of degrees of freedom is achieved by the use of orthogonal sets of Ritz functions. The reduced system of equations is uncoupled and solved very efficiently using the complex eigenvectors. A numerical example consisting of the response of a structure resting on a homogeneous half‐space is solved using the new method and one of the approaches in the frequency domain. Results given by both methods are remarkably similar.

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 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.

The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions.

The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE).

The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach.

Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.

Optimisation of the discretising steps in the space and time domains has been studied for the evaluation of corresponding optimum value of over‐relaxation parameter in the numerical solution of transient heat flow equation using successive‐over‐relaxation method in the finite difference code. No closed form solutions are available for the optimisation of a complete set of involved parameters in such problems. The present work deals quantitatively with the need for a more generalised closed form relation involving discretising steps in the space and the time domains for an optimal over‐relaxation parameter. The maximum finite difference error and the number of iterations required to achieve a reasonable error tolerance in the functional value are the two criteria used to obtain an optimised set of parameters. The effect of deviation from the optimised values of any of the involved parameters has been shown over a model problem of one‐dimensional diamond‐IIa medium of 100 micrometer length and for a time duration of 1.24 micro‐seconds.