Yun Yi

Efficient Implementation for the Unconditionally Stable 2-D WLP-FDTD Method

This letter presents an efficient algorithm for the unconditionally stable two-dimensional finite-difference time-domain method with weighted Laguerre polynomials (2-D WLP-FDTD). The huge sparse matrix equation is solved with a factorization-splitting scheme. This leads to much less CPU time and memory storage than those in the conventional implementation. To verify the accuracy and efficiency of the proposed method, two numerical examples are given.

Unconditionally Stable ADI–BOR–FDTD Algorithm for the Analysis of Rotationally Symmetric Geometries

In this letter, the alternating-direction-implicit (ADI) technique is applied to the body of revolution finite-difference time-domain (BOR-FDTD) method, resulting in an unconditionally stable ADI-BOR-FDTD. It inherits the advantages of both ADI-FDTD and BOR-FDTD methods, i.e., not only eliminating the restraint of the Courant-Friedrich-Lecy condition, with an efficient saving of CPU running time, but also leading to a significant memory reduction in the storage of the field components. To overcome the singularity, a special treatment is made along the vertical axis of the cylindrical coordinates. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm

TF/SF Boundary and PML–ABC for an Unconditionally Stable FDTD Method

This letter proposes a total-field/scattered-field (TF/SF) formulation and perfectly matched layer (PML) absorbing boundary condition for the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs). This approach provides the computational flexibility in electromagnetic scattering and improved performance yet maintains unconditional stable. Numerical results show the TF/SF connecting boundary and PML are effective in the WLP-FDTD method for scattering

A new 2-D FDTD method applied to scattering by infinite objects with oblique incidence

A new two-dimensional (2-D) finite-difference time domain (FDTD) method applied to scattering by infinite objects with oblique incidence is proposed. 2-D Maxwells equations, differential equations, and perfectly matched layer (PML) absorbing boundary conditions (ABC) are derived. The incident wave, computed by the 1-D FDTD method, is set on the connecting boundary. The accuracy and the efficiency of the proposed method have been verified by comparing the results of the split-field periodic FDTD method, the sine-cosine method, and the transmission line theory method with the proposed method.

A New Efficient Algorithm for 3-D Laguerre-Based Finite-Difference Time-Domain Method

We previously introduced a new efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. The new 2-D efficient algorithm is based on the use of an iterative procedure to reduce the splitting error associated with the perturbation term, and it does not involve any nonphysical intermediate variables. Numerical results indicated that the new efficient algorithm shows better performance for modeling some regions with larger spatial derivatives of the field. In this paper, we extend this approach to a full 3-D wave. Numerical formulations of the new 3-D Laguerre-based FDTD method are devised and simulation results are compared to those using the conventional 3-D FDTD method and the alternating-direction implicit (ADI) FDTD method. We numerically verify that, at the comparable accuracy, the efficiency of the proposed method with an iterative procedure is superior to the FDTD method and the ADI -FDTD method. Also, in order to verify the stability of the iterative procedure, we present a convergence analysis and a long-time simulation to it in the paper.

The Capacitance Thin-slot Formalism Revisited: An Alternative Expression for the Thin-Slot Penetration

The capacitance thin-slot formalism is investigated, in which the effective permittivity is found to be time varying while the effective permeability is nearly constant. Additionally, it is found that the effective permeability is not equal to the reciprocal of the effective permittivity. Based on the improved formalism of the field distributions and numerical results, an alternative expression is derived for the thin-slot penetration by modifying coefficients of the updating equations near the slot. High-resolution standard finite difference time domain method (FDTD) result and commercially available numerical tool FEKO result are presented in support of the new expression.

A New Iterative Algorithm for Efficient 3-D Laguerre-Based FDTD Method

This letter presents a new iterative algorithm for efficient 3-D Laguerre-based finite-difference time-domain (FDTD) method. A new perturbation term and the Gauss-Seidel method are introduced in the algorithm. The theoretical analysis in the frequency domain shows that the splitting error introduced by the new perturbation term grows slower than that of the original one at the high frequency range. The Gauss-Seidel iterative method is used in the iterative procedure to speed up the convergence further. Numerical results show that the new iterative algorithm achieves a comparable accuracy with three iterations comparing to the original one with eight iterations, and the whole CPU time is reduced to about 34.5% of the original one.

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.

FDTD Calculation Model for the Transient Analyses of Grounding Systems

Transient performance of grounding systems is simulated using the finite-difference time-domain (FDTD) method for solving Maxwells equations. The derivation of the transient current is first adjusted to obtain accurate impedance. Then, the FDTD calculation model is optimized to predict the grounding system impedance accurately without resulting in huge computational resources. From evaluation, the direction parallel to the connecting line is supposed to integrate the transient voltage. The transient voltage should be integrated 20 m in length and the reference electrode to be 30 m from the grounding system, and these lengths should be further enlarged for a large dimension grounding system. The transient impedance of the five lightning current components is very close to each other except the multiple burst, and the current should be injected close to the ground.

One-Step Leapfrog ADI-FDTD Method in 3-D Cylindrical Grids With a CPML Implementation

A three-dimensional (3-D) unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method in the cylindrical coordinate system is presented. It is more computationally efficient while preserving the properties of the two-step scheme. By reusing the auxiliary variable, it also uses less memory than the two-step scheme. In contrast with the one-step leapfrog ADI-FDTD method in the Cartesian coordinate system, some implicit equations of the one-step leapfrog ADI-FDTD method in the cylindrical coordinate system are not tridiagonal equations. The Sherman Morrison formula is used to solve them efficiently. To solve open region problems, convolutional perfectly matched layer (CPML) for the one-step leapfrog scheme is proposed. Numerical results are presented to validate them.