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The recently developed two-directional unconditionally stable single-field (US-SF) finite-difference time-domain (FDTD) method is generalized to a 3-D. The method is based on the application of the Crank–Nicolson scheme to only one of Maxwell curl equations which leads to an unconditionally stable finite-difference solution of the 3-D vector wave equation in the time domain. The method is designated as a single field because only the electric (or magnetic) field is updated in each time step. The implicit equations for each time step can be solved using a tridiagonal matrix algorithm without a need for matrix inversion. To achieve this, we introduced a new modified time-splitting scheme for the multilevel difference equations. Unlike the existing time-splitting method used to solve such equations which results in instability when dealing with inhomogeneous media, the presented method remains stable. As an important feature of the proposed US-SF-FDTD method, the updating of the three field components can be executed simultaneously (in parallel) by applying multithreading, thereby significantly reducing runtime. The unconditional stability of the proposed method is proved analytically. The accuracy and computational efficiency of the proposed method are demonstrated by providing numerical examples and by comparison to other FDTD methods and to the analytic solution when available. [ABSTRACT FROM AUTHOR]

A novel finite-difference solution of the time-domain three-dimensional wave equation with a stability criterion relaxed from the discretization space steps in two directions is presented. This method is particularly useful and efficient for electromagnetic simulation of structures having fine details in two Cartesian directions. During the algorithm iteration process, updating of only the electric field is required. In comparison to other weakly conditional finite-difference time-domain (WCS-FDTD) algorithms, the proposed method is shown to be computationally more efficient in terms of runtime because the implicit updating equations can be solved simultaneously (in parallel) by applying multithreading, while in the earlier WCS-FDTD methods, a simultaneous solution of the implicit updating equations was not feasible. The high computational efficiency and accuracy of the proposed method is demonstrated by producing several numerical examples and providing comparison to the results obtained using methods available in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a new 3-D hybrid implicit explicit (HIE) finite-difference time-domain (FDTD) method with a stability criterion relaxed from the discretization space steps in one direction. The proposed method is particularly useful and efficient for electromagnetic (EM) simulation of structures having fine details in one Cartesian direction such as thin shields and thin slots on a metallic enclosure whose EM analysis are popular and important in electromagnetic compatibility. In this algorithm, unlike common FDTD methods in which both electric and magnetic fields are updated, only the electric field needs to be updated during the time-marching process of the algorithm; hence, it is called as a “single-field” FDTD method. This could be achieved by applying the Crank—Nicolson (CN) scheme only to the electric field, while in earlier HIE-FDTD (and also unconditionally stable FDTD) methods, the CN scheme is applied to both electric and magnetic fields. The proposed algorithm consists of two implicit and three explicit updating equations that can be solved simultaneously (in parallel) by applying multithreading. Thanks to few and simple updating equations of the proposed algorithm, it is computationally more efficient than other HIE-FDTD methods in terms of runtime. The high computational efficiency and accuracy of the proposed method are demonstrated by producing several numerical examples and providing comparison to the results obtained using methods available in the literature. [ABSTRACT FROM AUTHOR]

A cost-effective approach to the finite-difference time-domain (FDTD) modeling of magnetized graphene sheets as a dispersive anisotropic conductive surface is proposed. We first introduce a novel method for implementation of anisotropic conductive surface boundary condition in the FDTD method. Then, by applying the surface conductivity matrix of magnetized graphene, we present modeling magnetized graphene as an infinitesimally thin conductive sheet in the FDTD method. The applicability, accuracy, and stability of the method are demonstrated through numerical examples. The proposed approach is validated by comparing the results with existing analytic solution. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for modeling of electrically thin conductive shields in the finite-difference time-domain (FDTD) method. The method is based on representation of the relation between the fields at two faces of the shield as an impedance boundary network condition (INBC) in the frequency domain. The INBC includes frequency-dependent self and mutual impedances which are approximated by series of partial fractions in terms of real or complex conjugate pole-residue pairs. A discrete time-domain INBC at the shield is generated, which is then incorporated within the FDTD method. The primary advantages of the proposed approach are: 1) the convolution equations are not used in the formulation, 2) the approximation applied for discretizing the Maxwell equation has second-order accuracy in time and first-order of accuracy in space, and 3) the stability of the method is governed by the classical Courant Friedrichs Lewy stability condition. Numerical examples are presented to validate the new method and to demonstrate its efficiency and accuracy. [ABSTRACT FROM PUBLISHER]

In this paper, we present a method to incorporate the intraband and interband terms of the surface conductivity of graphene into the finite-difference time-domain (FDTD) method. The method is based on approximating the surface resistivity of graphene by a series of partial fractions in terms of real or complex conjugate pole–residue pairs. Then, a discrete time-domain surface boundary condition at the graphene sheet is generated, which is then incorporated within the FDTD method using the infinitesimally thin sheet formulation. Numerical examples are presented to validate and demonstrate the capabilities and advantages of the proposed approach. [ABSTRACT FROM PUBLISHER]

In [1], rx , ry , and \textbf G\textbf {M} were mistyped. The correct values are \begin{align*} r_{x}=&\frac {\sqrt {2} \Delta t}{\sqrt {\varepsilon \mu } \Delta x} \sin {\left ({\frac { k_{x} \Delta x}{2} }\right )}\\ r_{y}=&\frac {\sqrt {2} \Delta t}{\sqrt {\varepsilon \mu } \Delta y} \sin {\left ({\frac { k_{y} \Delta y}{2} }\right )}\\ \mathbf {G_{M}}=&\begin{matrix} \left [{ \begin{matrix} \big (1+r_{x}^{2}\big )(\xi ^{2}+1)-2\xi &\quad -(2r_{x} r_{y}) \xi \\ -(2r_{x} r_{y}) \xi &\quad \big (1+r_{y}^{2}\big )(\xi ^{2}+1)-2\xi \end{matrix} }\right ]. \end{matrix} \end{align*} [ABSTRACT FROM AUTHOR]