A Novel Algorithm in FDTD analysis of Target Containing ‘Infinitely Thin’ Graphene Sheet

A series of atomistic molecular dynamics simulations were performed for 4-mer isoprene molecules confined between graphene sheets with varied graphene separations in order to observe the finite size effects arose from the van der Waals interactions between the isoprene oligomer, forming high density shells at the graphene interfaces. For the small confinement regions, 1.24 nm and 2.21 nm, local density of isoprene at the graphene interface becomes higher than 10 times the bulk density. These results provided the further insights towards the rational design of nanostructures based on graphene sheets and natural rubber polymer.

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing

FDTD fundamentals Introduction A fundamental quest in electromagnetics and antenna engineering is to solve Maxwell's equations under various specific boundary conditions. In the last several decades, computational electromagnetics has progressed rapidly because of the increased popularity and enhanced capability of computers. Various numerical techniques have been proposed to solve Maxwell's equations [1]. Some of them deal with the integral form of Maxwell's equations while others handle the differential form. In addition, Maxwell's equations can be solved either in the frequency domain or time domain depending on the nature of applications. The success in computational electromagnetics has propelled modern antenna engineering developments. Among various numerical techniques, the finite difference time domain (FDTD) method has demonstrated desirable and unique features for analysis of electromagnetic structures [2]. It simply discretizes Maxwell's equations in the time and space domains, and electromagnetics behavior is obtained through a time evolving process. A significant advantage of the FDTD method is the versatility to solve a wide range of microwave and antenna problems. It is flexible enough to model various media, such as conductors, dielectrics, lumped elements, active devices, and dispersive materials. Another advantage of the FDTD method is the capability to provide a broad band characterization in one single simulation. Since this method is carried out in the time domain, a wide frequency band response can be obtained through the Fourier transformation of the transient data. Because of these advantages, the FDTD method has been widely used in many electromagnetic applications.

Recently, the FDTD (Finite Difference Time Domain) method, which directly solves Maxwell's equations, has been applied to lightning surge problems involving electrical wires in three-dimensional arrangements, such as power and telecommunication circuits. Lightning arresters are installed to protect the circuits from abnormal voltages due to lightning, for example. We have already proposed a technique for representing a lightning arrester in the FDTD method. However, this technique simply represents the V-I characteristics of the arrester using just three parameters and requires a method for avoiding the numerical oscillation due to the nonlinear characteristics of the arrester.In this paper, we propose a new technique for representing the V-I characteristics of the arrester in detail using the piecewise linear function defined by several points and for improving the numerical stability without the method for avoiding the numerical oscillation. Using a test circuit, the proposed technique is validated by comparing the results calculated by the FDTD method with those by the EMTP (ElectroMagnetic Transients Program) which is a circuit-theory-based simulation program. Finally, as an example of applying the proposed technique, we calculate lightning-induced voltages on a distribution line with a lightning arrester. The calculated results by the FDTD method agree well with those by a conventional method based on circuit theroy.

In this letter, a three-dimensional finite-difference time-domain (FDTD) method that is second-order in time and fourth-order in space on a face-centered cubic (FCC) grid, termed as FCC-FDTD(2,4), is proposed to solve the time-domain Maxwell's equations. The proposed method shows a much lower numerical dispersion error compared with the errors of other FDTD schemes, such as the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. This improvement in the numerical dispersion results from the FCC grid and the fourth-order scheme in space used in the proposed FCC-FDTD(2,4) method. Then, the Courant-Friedrichs-Lewy condition is given through spectral analysis, and an analytical numerical dispersion relation is obtained and comprehensively studied through numerical results with the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. Compared with the other three FDTD methods, the proposed method has much smaller numerical dispersion errors. Finally, the accuracy of the proposed method is further validated with other numerical examples.

An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain (FDTD) method for simulating Maxwell's equations for one-dimensional systems is presented. The method uses d'Alembert's splitting of waves into forward and backward pulses of arbitrary shape and allows for grid spacing and material properties that vary with the position. Constant velocity of waves in dispersionless dielectric materials, partial reflection and transmission at boundaries between materials with different indices of refraction, and partial reflection, transmission, and attenuation through conducting materials are derived without recourse to exponential functions, trigonometric functions, or complex numbers. Placing d'Alembert's method on a grid is shown to be equivalent to the FDTD method and allows for simple and visual proof that the FDTD method is exact for dielectrics when the ratio of the spatial and temporal grid spacing is the wave speed, a straightforward way to incorporate reflectionless boundary conditions and a derivation that the FDTD method retains second-order accuracy when the grid spacing varies with the position and the material parameters make sudden jumps across layer boundaries.

If a return stroke occurs nearby a distribution line, the electromagnetic field radiated by the return-stroke current induces voltages on the distribution line. A lightning arrester is often applied to the distribution line to suppress such overvoltage. In this study, the finite difference time domain (FDTD) method, in which Maxwell's equations are solved directly, is applied to the calculation of the lightning-induced voltages on the distribution line. We calculate lightning-induced voltages on a distribution line with a lightning arrester and compare the results calculated by the FDTD method with those obtained by a conventional method based on circuit theory for validation purposes. Moreover, we calculate the lightning-induced voltages on a three-phase distribution line with lightning arresters and a grounding wire.

A new approach to wave oriented radio propagation modeling based on extended finite difference time domain (FDTD) method has been developed. In order to model radio wave propagation using standard FDTD, the entire propagation path would need to be included in the FDTD grid. This would require prohibitive amount of computer memory and time. The new approach takes advantage of the fact that when a pulsed radio wave propagates over a long distance the significant pulse energy exists only over a small part of the propagation path at any instant of time. This allows the use of a relatively small FDTD computational mesh that exists only over a portion of the propagation path and move along with the pulse. At the leading edge of the FDTD mesh inside the moving window the appropriate terrain, foliage, and atmospheric parameters are added to the mesh. At the trailing edge the terrain and foliage that have been left behind by the pulse are removed. Since this method solves Maxwell's equation directly, all physics relevant to radio wave propagation is included in this model In addition, since it is based on the FDTD method, this model can take advantage of the extensive research that has been done on the FDTD algorithm, such as the higher-order finite differencing and multiresolution time domain (MRTD). The moving window FDTD (MWFDTD) method has previously been applied to propagation over different types of irregular terrain. This paper extends this approach to forest covered terrain by treating the foliage as a lossy dielectric layer. In addition, using MWFDTD, atmospheric refractive effects can also be included simultaneously with irregular terrain effects and foliage. We apply our method to radio wave propagation in atmospheric ducts. Comparisons with path loss measurements show good accuracy and illustrate the advantages of a full wave method. While this method is slower than other propagation models, it is potentially much more accurate. Therefore, MWFDTD can be used to validate other faster propagation models, and can provide predictions in cases where a high degree of accuracy is desired.

We investigated the role of graphene interfaces in strengthening and toughening of the Cu-graphene nanocomposite by a combination of in situ transmission electron microscopy (TEM) deformation and molecular dynamics (MD) simulations. In situ TEM directly showed that dislocation plasticity is strongly confined within single Cu grains by the graphene interfaces and grain boundaries. The weak Cu-graphene interfacial bonding induces stress decoupling, which results in independent plastic deformation of each Cu layer. As confirmed by the MD simulation, the localized deformation made by such constrained dislocation plasticity results in the nucleation and growth of voids at the graphene interface, which acts as a precursor for crack. The graphene interfaces also effectively block crack propagation promoted by easy delamination of Cu layers dissipating the elastic strain energy. The toughening mechanisms revealed by the present study will provide valuable insights into the optimization of the mechanical properties of metal-graphene nanolayered composites.

This study proposes a method for modelling of the graphene sheets using a finite-difference time-domain method based on Laplace transform current density convolution. The modelling of the graphene sheets is achieved by using their effective conductivity when placed in a finite-difference time-domain lattice and applying Laplace transform for obtaining tangential current density on the graphene sheet and associated recursive Maxwell's equations of the tangential electric field components on the graphene sheet. The proposed numerical formulation is validated by comparing it with the analytical results. A design example of the periodic structure is developed to investigate the behaviour of the graphene sheets and its application is proposed for the reconfigurable terahertz graphene antennas.

A new hybrid finite-difference time-domain (FDTD) and mixed potential integral equation (MPIE) method is proposed for the modeling of multilayer planar circuits with locally inhomogeneous objects. By using equivalence principle, the original problem can be decomposed into two kinds of regions. The FDTD method is employed to model the locally inhomogeneous objects and construct an interaction matrix to be used in the subsequent model coupling procedure. The MPIE method with less singular kernels is applied to model the layered structure with possible perfect electric conductors. The FDTD model and the MPIE model are coupled together by enforcing the continuity of the tangential electric and magnetic fields on the equivalent surface using a Galerkin testing procedure. Numerical results are presented to validate the proposed hybrid FDTD-MPIE method.

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Summary form only given. The simplest boundary condition to implement in a finite difference time domain (FDTD) code is that of the perfect conductor where the tangential electric field and the normal magnetic field are set to zero. However, many problems require a lossy boundary. This is often implemented with the creation of a layer of cells within the metal that are given a finite conductivity. Resolving the skin depth in these cells may require using cells that are much smaller than those in the rest of the problem domain. This may reduce performance by requiring a smaller time step to satisfy the Courant condition. It also adds complexity to the code and to required input. Using a surface boundary condition (rather than a volume boundary condition) is potentially more efficient and easier to implement and use. This type of boundary often suffers the difficulty of requiring a time history of the magnetic field which for problems with large boundaries and/or many time cycles can lead to prohibitively large memory requirements. We propose a finite conductivity surface boundary condition that is easy to implement and has very little computational overhead. Preliminary tests show the method to be stable and to damp fields in a predictable way. However, quantitative agreement with analytic theory for simple test problems requires the use of a non-physical problem-specific parameter by the user.

Three-dimensional finite-difference time domain (FDTD) and pseudospectral time-domain (PSTD) algorithms, with perfectly matched layer absorbing boundary condition, are presented for nonmagnetized plasma as a special case of general inhomogeneous, dispersive, conductive media. The algorithms are tested for three typical frequency bands, and an excellent agreement between the FDTD/PSTD numerical results and analytical solutions is obtained for all cases. Several applications, such as laser-pulse propagation in plasma hollow channels, surface-wave propagation along a plasma column of finite length, and energy deposition of electron cyclotron resonance plasma source, demonstrate the capability and effectiveness of these algorithms. The PSTD algorithm is more efficient and accurate than the FDTD algorithm, and is suitable for large-scale problems, while the FDTD algorithm is more suitable for fine details. The numerical results also show that plasma has complex transient responses, especially in the low-frequency and resonance regimes. Because of their flexibility and generality, the algorithms and computer programs can be used to simulate various electromagnetic waves-plasma interactions with complex geometry and medium properties, both in time and frequency domains.

We investigate thermal effects in the human head exposed to the electromagnetic (EM) radiation of a mobile antenna at 0.9 GHz frequency. Computer simulation of EM and thermal phenomena in the given problem was performed. The simulation code is based on the finite-difference time-domain (FDTD) method for Maxwell's equations (Taflove, A. and Hagness, S., "Computational Electrodynamics: the finite difference time-domain method", 2nd edition, Artech House, 2000) and bio heat equations (Bernardi, P. and Pisa, S., IEEE Trans. Microwave Theory Tech., vol.48, p.1118-26, 1998) for the EM and thermal problems respectively.