Yunfei Mao

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

This paper combines a hybrid implicit-explicit (HIE) method with spectral flnite-difierence time-domain (SFDTD) method for solving periodic structures at oblique incidence, resulting in a HIE-SFDTD method. The new method has the advantages of both HIE-FDTD and SFDTD methods, not only making the stability condition weaker, but also solving the oblique incident wave on periodic structures. Because the stability condition is determined only by two space discretizations in this method, it is extremely useful for periodic problems with very flne structures in one direction. The method replaces the conventional single-angle incident wave with a constant transverse wave-number (CTW) wave, so the flelds have no delay in the transverse plane, as a result, the periodic boundary condition (PBC) can be implemented easily for both normal and oblique incident waves. Compared with the ADI-SFDTD method it only needs to solve two untridiagonal matrices when the PBC is applied to, other four equations can be updated directly, while four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in the ADI-SFDTD method. Numerical examples are presented to demonstrate the e-ciency and accuracy of the proposed algorithm. Results show the new algorithm has better accuracy and higher e-ciency than that of the ADI-SFDTD method, especially for large time step sizes. The CPU running time for this method can be reduced to about 45% of the ADI-SFDTD method.

A SIMPLE LOCAL APPROXIMATION FDTD MODEL OF SHORT APERTURES WITH A FINITE THICKNESS

This paper brings forward a simple local approximation flnite-difierence time-domain (FDTD) method for the analysis of short apertures with a flnite thickness. By applying the equivalence principle together with a simple local approximation, the varying fleld distribution is accurately derived. The updating equations for the slot fleld can be derived by casting the fleld distributions into the contour paths containing the apertures. The method has been applied to two problems and the results are compared with the high-resolution standard FDTD simulation results and the measurement results. The accuracy of the proposed method is verifled from the comparison of both the fleld distribution and the time-domain and frequency-domain slot coupling results. It is demonstrated that the local approximation is highly e-cient and timesaving, and the present method is stable, numerically and computationally e-cient.

Unconditionally Stable SFDTD Algorithm for Solving Oblique Incident Wave on Periodic Structures

In this letter, the alternating-direction-implicit (ADI) technique is applied to spectral finite-difference time-domain (SFDTD) method, resulting in an ADI-SFDTD method. It holds the advantages of both ADI-FDTD and SFDTD, not only eliminating the restriction of the Courant-Friedrich-Levy (CFL), but also solving the oblique incident wave on periodic structures conveniently. In order to save the CPU running time, the Sherman-Morrison formula is used to solve the untridiagonal linear systems. To reduce the numerical dispersion error, the optimized procedure is also applied. The accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.

FDTD Modeling of the Earthing Conductor in the Transient Grounding Resistance Analysis

The grounding system plays an important part in the lightning protection system of power and communication systems. The finite-difference time-domain (FDTD) method is widely used in modeling complex electromagnetic interaction problems. However, it is difficult to model the earthing conductor using the standard FDTD method in the transient grounding resistance (TGR) analysis for the electrically small depth of the earthing conductors. In this letter, a new method has been proposed to model the earthing conductor by incorporating the singularities of the field variation near the conductor into the Faradays contour path. The efficiency of the proposed model has been approved by verifying both the supposed field distribution near the earthing conductor and the TGR.

WCS-FDTD Algorithm for Periodic Structures

In this letter, the weakly conditional technique is applied to the finite-difference time-domain (FDTD) method, called WCS-FDTD in short. It is combined with periodic boundary condition (PBC), so periodic structures can be solved by using this method conveniently. When the explicit difference calculations are performed in the directions with larger spatial increments, the time-step is thus determined by the larger spatial increments, and the stability condition is less strict than the conventional FDTD method. In order to save the CPU running time, the Sherman-Morrison formula is used to solve the nontridiagonal linear systems. Compared to ADI-FDTD method, this method has better accuracy and computational efficiency. Numerical results are given to demonstrate the effectiveness of the proposed method.

Application of the Leapfrog ADI FDTD Method to Periodic Structures

In this letter, the one-step leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method has been introduced to solve periodic structures, resulting in a one-step leapfrog periodic ADI-FDTD method. In comparison to the original ADI-FDTD method, the one-step leapfrog ADI-FDTD method retains almost the same numerical modeling accuracy, but with higher computational efficiency. To simplify the issue, a reformation of the periodic one-step leapfrog ADI-FDTD method is also presented. Numerical results are given to demonstrate the proposed formulation. It is found that the periodic one-step leapfrog ADI-FDTD method requires less memory and CPU time than the conventional periodic ADI-FDTD method. To reduce the numerical dispersion error, an optimization procedure is applied.

A Novel Weakly Conditionally Stable FDTD Method for Periodic Structures

In this letter, a novel weakly conditionally stable finite-difference time-domain (FDTD) method for solving periodic structures is presented, which is extremely useful for periodic problem with thin slots in one or two directions. To verify the validity of the proposed formulations, a numerical example of electromagnetic band-gap (EBG) structure with thin slots is given. Compared to the alternating-direction implicit FDTD (ADI-FDTD) method, the presented method has higher accuracy and efficiency. Results show the running time can be reduced to about 2/3 of the periodic ADI-FDTD method in the same simulation. To reduce the numerical dispersion error, the optimized procedure is applied.

A numerical study on bow shocks around the lightning return stroke channel

Bow shock structures are important to various hydrodynamics and magnetohydrodynamics (MHD) phenomena in geophysics and astrophysics. The formation and propagation of bow shocks around the lightning return stroke channel are investigated based on the self-similar motion theory and simulated with a two-dimensional Eulerian finite volume resistive radiation MHD code. In this framework, as verification of theoretical models, the evolving structures of many quantities, such as the plasma density, temperature, pressure, shock velocity, and magnetic field, can be obtained, which present all the characteristics of bow shocks in the lightning return stroke processes. The evolution characteristics and the configuration of the curved return stroke channels, e.g., the non-ideal effects and the scaling laws, are discussed in detail. The results may have applications for some observed features of the return stroke channels and other phenomena in the lightning discharge plasmas.

Parallel implementation of the split-field FDTD method for the analysis of periodic structure

The periodic structure can be analyzed by using the split-field FDTD method. But when the very fine grid is involved, more memory and time are required, sometimes it even canpsilat be calculated on single PC machine. In this paper we present the parallel implementation of the split-field FDTD method based on the message passing interface(MPI), which solves the memory and speed problems, and give out a new method based on the conversation of energy, so as to verify the accuracy and the efficiency. We also compare the results of the serial split-field method with the proposed method.

A novel TF/SF boundary for cylindrical FDTD method with ground

The finite-difference time-domain (FDTD) method is proposed as a means of accurately computing electromagnetic scattering by an external plane wave. The total-field/scattered-field (TF/SF) formulation resulted from attempts to realize a plane-wave source that avoids the difficulties caused by using either hard sources or the initial-condition approach. It is very complicated to get the closed form of the incident fields with ground for a pulse plane wave. In this letter, we carry out the formulations of TF/SF boundary with the ground for the cylindrical FDTD. Numerical examples verify that the presented method can solve the incident wave with ground conveniently and accurately.