Hai-Lin Chen

Using a Two-Step Finite-Difference Time-Domain Method to Analyze Lightning-Induced Voltages on Transmission Lines

A novel high-efficient two-step finite-difference time-domain (FDTD) method is proposed to analyze the lightning-induced voltages on transmission lines (TLs) in this paper. The proposed method includes two steps. The first step is to calculate, using the 2-D FDTD method, electromagnetic fields that are radiated from a vertical lightning channel and illuminate the nearby TLs. The second step is to calculate, using the 3-D FDTD method, the electromagnetic response of the TL that is illuminated by the incident electromagnetic fields added at the total field-scattered field connecting the boundary of the 3-D space. To validate the proposed two-step FDTD method, the results calculated using the two-step FDTD method are compared with those calculated with Agrawal coupling model, and with those calculated using the 3-D FDTD method. The two-step FDTD method shows high computational efficiency in analyzing lightning-induced voltages on TLs.

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

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.

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.

An Unconditionally Stable One-Step Leapfrog ADI-BOR-FDTD Method

In this letter, an unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for body of revolution (BOR) is proposed. It is more computationally efficient while preserving the properties of the original alternating-direction-implicit body of revolution finite-difference time-domain (ADI-BOR-FDTD) method. Due to the singularity, some field components on and adjacent to the axis are treated especially. To verify the accuracy and efficiency of the method, the scattered field from a PEC cylinder with a notch is calculated.

An Unconditionally Stable Radial Point Interpolation Method Based on Crank–Nicolson Scheme

This letter presents a novel unconditionally stable radial point interpolation meshless method. With the application of the Crank–Nicolson scheme, an implicit time-stepping formulation for the proposed method is derived. Numerical experiment is implemented to demonstrate the effectiveness of the code, and the obtained result is compared to results of other methods.

Study of Periodic Structures at Oblique Incidence by Radial Point Interpolation Meshless Method

This paper presents a novel split-field radial point interpolation meshless (RPIM) scheme for the study of periodic structures under oblique incidence condition. The time delay in the transverse plane is eliminated with the introduction of a set of auxiliary variables. With the application of split-field technique to the standard RPIM method, a leap-frog formulation is derived. Numerical experiment is implemented to demonstrate the effectiveness of the code and the obtained result is compared with result of split-field finite-difference time domain method.

PML Absorbing Boundary Condition for Efficient 2-D WLP-FDTD Method

In this letter, Berengers perfectly matched layer (PML) absorbing boundary condition is presented for the efficient two-dimensional (2-D) finite-difference time-domain (FDTD) method with weighted Laguerre polynomials. Through adding a perturbation term, the huge sparse matrix equation is solved with a factorization-splitting scheme. To verify the validity of the proposed formulations, a numerical example of scattering from a 2-D rectangular conductor is given.

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.