Weakly Conditionally Stable Finite-difference Time-domain Research Articles

A novel hybrid algorithm based on FDTD and WCS‐FDTD methods

In this article, a hybrid algorithm based on traditional finite-difference time-domain (FDTD) and weakly conditionally stable finite-difference time-domain (WCS-FDTD) algorithm is proposed. In this algorithm, the calculation domain is divided into fine-grid region and coarse-grid region. The traditional FDTD method is used to calculate the field value in the coarse-grid region, while the WCS-FDTD method is used in the fine-grid region. The spatial interpolation scheme is applied to the interface of the coarse grid region and fine grid region to insure the stability and precision of the presented hybrid algorithm. As a result, a relatively large time step size, which is only determined by the spatial cell sizes in the coarse grid region, is applied to the entire calculation domain. This scheme yields a significant reduction both of computation time and memory requirement in comparison with the conventional FDTD method and WCS-FDTD method, which are validated by using numerical results.

Using WCS-FDTD Method to Study the Plasma Frequency Selective Surface

The plasma is very useful to design the dynamically tunable Frequency Selective Surface (FSS) because of its tunable property. But it is difficult to simulate the plasma FSS by using the conventional finite-difference time-domain (FDTD) method, because the FSS often has fine structure which confines the time step size. To solve this problem, the weakly conditionally stable finite-difference time-domain (WCS-FDTD) method is developed in this paper. The WCS-FDTD method uses auxiliary difference equation to represent plasma's dispersive characteristic, and removes the confinement of FSS's fine structure on time step size by using hybrid implicit-explicit (HIE) technique. So, compared with the FDTD method, the presented method can save a large number of computational time, which are validated by numerical examples. Also, by using the proposed method, the tunability of plasma FSS are validated and analyzed numerically.

Analyzing Graphene-Based Absorber by Using the WCS-FDTD Method

A weakly conditionally stable finite-difference time-domain (WCS-FDTD) method is used to simulate a graphene-based absorber. By using the auxiliary differential equation and Pade fitting method, both the interband and intraband conductivities of the graphene are incorporated into the WCS-FDTD method. The time step increment in the proposed method is not determined by the fine meshes in the graphene layer, so the computational efficiency of this method is greatly improved from that of the conventional FDTD method. By using the proposed WCS-FDTD method, a graphene-based absorber is simulated and analyzed. The numerical result shows that the graphene can achieve tunable absorption through controlling its chemical potential, and the interband conductivity of the graphene has important effects on the performance of the absorber.

The WCS‐FDTD method for simulating graphene

AbstractA weakly conditionally stable‐finite difference time‐domain (WCS‐FDTD) scheme to simulate graphene is developed. The Pade fit method is used to approximate the interband conductivity of graphene and introduced into the WCS‐FDTD method directly by using the auxiliary differential equation. The accuracy of the Pade method is verified, and the effect of chemical potential on the accuracy is discussed. The time step size in proposed method is only determined by one spatial cell size, so the computational efficiency of this method is considerably larger than those of the conventional FDTD method and implicit explicit‐finite (HIE)‐FDTD method. An infinite graphene sheet and a graphene‐based metal sheet are simulated by using presented method, and the results are compared with theoretical value and the numerical results of the conventional FDTD method and HIE‐FDTD method. Simulated results show that proposed WCS‐FDTD method has high accuracy, and compared with the FDTD method and HIE‐FDTD method, its computational time is largely shorted. Besides, the numerical example presents that the interband conductivity has important effect on the performance of the graphene at high‐frequency range, especially when the chemical potential is small.

A dispersive WCS-FDTD method for simulating graphene-based absorber

A dispersive weakly conditionally stable finite-difference time-domain (WCS-FDTD) method for the efficient simulations of the graphene-based absorbers with fine structures in two directions is proposed in this paper. It is based on the auxiliary differential equation technique and the hybrid implicit explicit difference technique. The maximum time step size of this method is only determined by the largest spatial discretization. The numerical results demonstrate that the dispersive WCS-FDTD method has high computational accuracy and the computational time is greatly reduced compared with the dispersive FDTD method and the dispersive HIE-FDTD method.

Efficiency-Improved 3-D WCS-FDTD Algorithm for Periodic Structures at Oblique Incidence

For solving the problems of oblique incident wave on periodic structures, an efficiency-improved 3-D weakly conditionally stable finite-difference time-domain (WCS-FDTD) method is presented in this letter, whose Courant–Friedrichs–Lewy (CFL) stability condition is only determined by one space step size. By expressing the extra terms caused by the phase delay as the form of the coefficient matrix, and combining with the locally one-dimensional (LOD) scheme and the inverse matrix operator, the Maxwell’s equations are split into two sub-step procedures. Further, by introducing a set of auxiliary field variables denoted by ${\psi}$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical example demonstrates that the proposed method is more efficient while keeping the same CFL stability condition and memory storage requirement as that of the existing method.

One‐step leapfrog weakly conditionally stable finite‐difference time‐domain method for body of revolution

In this study, a novel one-step leapfrog weakly conditionally stable finite-difference time-domain (WCS-FDTD) method for body of revolution (BOR) is presented. The singularity of some field components on and adjacent to the axis are solved specially, in accordance with the one-step leapfrog WCS-FDTD scheme. The electric and magnetic fields of the proposed method are interlaced half a time step apart and no sub-time steps are used. The novel method obtains a higher computational efficiency while preserving the properties of the conventional WCS-BOR-FDTD method. Its stability condition and dispersion error are presented analytically. Moreover, two numerical examples are given to demonstrate the proposed method.

Implementation of CPML for One-Step Leapfrog WCS-FDTD Method

In this letter, the convolutional perfectly matched layer (CPML) is modified and implemented for one-step leapfrog weakly conditionally stable finite-difference time-domain (WCS-FDTD) method. Since the WCS-FDTD method can be considered as an approximate factorization of the Crank—Nicolson scheme, the derived equations of CPML involve the calculation of auxiliary terms at two time steps which are different from that of conventional FDTD CPML method. To verify the effectiveness of proposed CPML, numerical investigation is performed and it is shown that, even with large Courant-Friedrich-Levy number (CFLN) chosen, the reflection error is still small and the electromagnetic field is stable.

An Efficient One-Step Leapfrog WCS-FDTD Method

For solving the electromagnetic problems with fine structures in two directions, this letter presents an efficient three-dimensional (3-D) one-step leapfrog weakly conditionally stable finite-difference time-domain (WCS-FDTD) method, in which the updating manner of field quantities is the same as that of the traditional FDTD method that electric and magnetic fields are calculated at every full time-step but interlaced half a step apart in both time and space. Furthermore, by introducing an auxiliary field variable group denoted by m, the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Compared to the original WCS scheme in Chen and Wang's work (IEEE Trans. Electromagn. Compat., vol. 49, no. 2, pp. 419-426, May 2007), the proposed method is more efficient while keeping the same numerical properties.

3D Weakly Conditionally Stable FDTD Method for Analyzing Periodic Structures

By dividing the 3D transformed Maxwell's equations into two parts and applying the Crank-Nicolson (CN) scheme to each part, four substep implicit procedures are obtained. After adjusting the order of four substeps, a weakly conditionally stable finite-difference time-domain (WCSFDTD) method is derived for solving the 3D problems of oblique incident plane wave on periodic structures. This method is very suitable for analyzing the problems which have fine structures in one or two directions, and the Courant-Friedrich-Levy (CFL) stability condition of it is more relaxed than that of the original held transformation methods. Numerical examples demonstrate that the presented technology is more efficient, especially at the high incident angle.

A novel PLRC-WCS FDTD method for dispersive materials

One-directional weakly conditionally stable finite-difference time-domain (WCS-FDTD) method is extended to solve electromagnetic problems in linear dispersive media by virtue of piecewise linear recursive convolution (PLRC) technique. This proposed method provides similar accuracy to PLRC alternating direction implicit (ADI) FDTD approach, yet consumes less computational time and less memory. This proposed method is particularly suitable for solving problems in linear dispersive materials with fine features along two spatial directions.

Using WCS‐FDTD method to simulate various cylindrical metallic enclosures

AbstractThe 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.

Using WCS‐FDTD method to simulate various small aperture‐coupled metallic enclosures

AbstractThe weakly conditionally stable finite‐difference time‐domain (WCS‐FDTD) method is employed to compute the electromagnetic coupling and shielding of various small aperture‐coupled metallic enclosures. In the WCS‐FDTD method, a larger time‐step size than allowed by the CFL stability condition limitation can be set because the algorithm of this method is weakly conditionally stable. Consequently, an increase in computational efforts caused by fine cells due to small apertures can be prevented. The results from the WCS‐FDTD method agree well with results from the conventional finite‐difference time‐domain (FDTD) method, and the required CPU time for the WCS‐FDTD method is much shorter than that for the FDTD method. Compared with the ADI‐FDTD method, the WCS‐FDTD method has better accuracy and higher efficiency, which is demonstrated by numerical examples. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1852–1858, 2007; Published online in Wiley Inter‐Science (www.interscience.wiley.com). DOI 10.1002/mop.22633