Zheng-Yu Huang

A New Unconditionally Stable Scheme for FDTD Method Using Associated Hermite Orthogonal Functions

An unconditionally stable solution using associated Hermite (AH) functions is proposed for the finite-difference time-domain (FDTD) method. The electromagnetic fields and their time derivatives in time-domain Maxwells equations are expanded by these orthonormal basis functions. By applying Galerkin temporal testing procedure to these expanded equations the time variable can be eliminated from the calculations. A set of implicit equations is derived to calculate the magnetic filed expansion coefficients of all orders of AH functions for the temporal variable. And the electrical field coefficients can be obtained respectively. With the appropriate translation and scale parameters, we can find a minimum-order basis functions subspace to approach a particular electromagnetic field. The numerical results have shown that the proposed method can reduce the CPU time to 0.59% of the traditional FDTD method while maintaining good accuracy.

Associated Hermite FDTD Applied in Frequency Dependent Dispersive Materials

An unconditionally stable frequency-dependent FDTD formulation for non-magnetized materials is developed using Associated Hermite (AH) expansion in this letter. By introducing orthogonal AH transform, the complex dielectric constant is transformed into AH domain and represented as a matrix form, and then incorporated into a set of implicit equations to calculate the expansion coefficients of electromagnetic fields. Numerical example shows that the result of the new algorithm is in consistent with the theoretical results.

Implementation of Associated Hermite FDTD Method to Periodic Structures

In this letter, we developed the unconditionally stable (US) associated Hermite (AH) finite-difference time-domain method for transient analysis of periodic structures at oblique incidence. With AH-domain differentiate operator and paralleling-in-order solution scheme, periodic Maxwells equations with complex frequency shifted perfectly matched layer are transformed to AH-domain five-point banded equation, which also unified the formula from total-field/scattered-field connection boundary and periodic boundary conditions. The numerical results verified the accuracy and efficiency of the proposed method when compared to the split-field method and US locally one-dimensional method.

Efficient Implementation for the AH FDTD Method With Iterative Procedure and CFS-PML

An efficient implementation for the associated Hermite finite-difference time-domain (AH FDTD) method with iterative procedure is proposed, which is an extension of previous works: the original and the paralleling-in-order-based AH FDTD methods. By introducing the alternating direction implicit method, the direct calculation of five-point matrix equation is replaced with iterative solving of tridiagonal matrices equations. For the 2-D case, only two tridiagonal matrixes need to be calculated in a full iterative cycle. In addition, the complex frequency shifted (CFS) perfectly matched layer (PML) is extended to the AH FDTD method and implemented together with this efficient solution scheme. Numerical examples show the superior computational performance of the proposed iterative procedure by comparison with the conventional FDTD method, the ADI FDTD method, and previous AH FDTD methods. The effectiveness of CFS-PML in AH FDTD is also verified.

Experimental study on the magnetic field shielding property of CFRP

The shielding effectiveness (SE) of carbon fiber reinforced polymer (CFRP) composite is investigated by a set of pulsed field generator considering the low-frequency magnetic near field produced by lightning. The incident filed is produced with a loop antenna driven by 12kA pulsed current and the field inside a 1m×1m×1m CFRP cavity is measured. Frequency domain transfer function of the shielding layer is analyzed based on time-domain measured waveforms. The result show CFRP has very small SE below 1MHz. The effect of such low frequency magnetic field within CFRP structure should be paid more attention in lightning protection.

A Modified INBC for FDTD Analyzing of Shielding Cavity with Thin Conductive Layers under plane wave incidence

A modified impedance network boundary condition (INBC) is proposed for modeling electrically thin conductive layers (TCLs) under plane wave incidence in finite-difference time-domain (FDTD) method. Compared to the conventional INBC which represents the relationship between the electric and the magnetic fields collocated at two faces of the TCL, the modified INBC takes into consideration both the half-space-cell and half-time-step difference of the electric and the magnetic fields in Yee’s grid. The primary advantage of the modified INBC is that it can be implemented in conventional FDTD algorithm without half-cell shift approximation. Numerical examples are presented to validate the efficiency and accuracy of the proposed method in analyzing thin layers with low conductivities.

Unconditionally Stable Associated Hermite FDTD With Plane Wave Incidence

In this letter, we developed a plane wave excitation formulation for the unconditionally stable Associated Hermite (AH) finite-difference time-domain (FDTD) method. By using a plane wave injector, the volume electric and magnetic current densities in Maxwells equations are expressed as an explicit form in AH domain to represent the incident field. An AH transformation matrix is designed to efficiently evaluate the expansion coefficients of the incidence plane wave at any point. Numerical example shows the results computed using the proposed formulation are in accordance with the solutions of the conventional FDTD method.