ADI-FDTD Formulation for General Dispersive Media

The current source implementation for the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is examined in this letter. By regarding the ADI-FDTD method as an approximate factorization of the Crank-Nicolson scheme, current source is naturally coupled into simulations. As a result, field distribution is much more improved and free of asymmetry.

An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods. However, its computational expenditure is found to be the lowest. In other words, in comparison with the ADI-FDTD and LOD-FDTD methods, the one-step arbitrary-order leap-frog ADI-FDTD method retains identical numerical modeling accuracy but with higher computational efficiency.

This paper describes the relaxation technique for the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. The ADI-FDTD method is computationally more complicate than the conventional FDTD and this method requires solving the tridiagonal matrix equation. Thus, this method may require more computational cost than the conventional method due to the large scale tri-diagonal matrix solution corresponding to a large number of meshes. In this paper, relaxation-based solution technique is discussed for the matrix solution and a simple numerical example is shown. As a result, it is confirmed that ADI-FDTD method with the relaxation technique is useful for the electromagnetic field simulation

A second-order in time and fourth-order in space, alternating direction implicit finite difference time domain (ADI-FDTD) scheme is presented for radio-wave propagation in a isotropic collisionless plasma. At the same time, the unconditional stability of the higher order ADI-FDTD formulation for plasma is analytically proved. By analysis of the growth factor, the numerical dispersion relation is derived. In addition, the numerical dispersion errors are investigated. From the error analysis and phase velocity data, it is argued that the proposed approach will significantly minimize the dispersion errors compared to the ADI-FDTD method.

A three-dimensional unconditionally-stable locally-one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed and is proved unconditionally stable analytically. In it, the number of equations to be computed is the same as that with the conventional three-dimensional alternating direction implicit FDTD (ADI-FDTD) but with reduced arithmetic operations. The reduction in arithmetic operations leads to approximately 20% less computational time in comparisons with the ADI-FDTD method.

In order to design a small antenna on the gallium arsenide monolithic microwave integrated circuit (MMIC), An H-shaped patch is designed. Initial experimental and theoretical characterization of the proposed structure has been carried out. It has been shown that the size of proposed patch antenna can be reduced to as low as one tenth of that of a half wavelength patch resonant at 6 GHz, saving significant substrate space. Ground plane truncation effects, which are important for MMIC applications, have been examined. Resonance frequency, radiation patterns and gain have been simulated by using the modified alternating-direction implicit finite-difference timedomain (ADI-FDTD) method.

In this paper, transient electromagnetic analysis of rectangular metallic enclosures with apertures illuminated by electromagnetic pulse (EMP) is investigated using alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The dispersive property of substrate of printed circuits boards (PCBs) is characterized by the Debye model. Numerical results shows that induced voltage of inner circuits are seriously affected by angle of incidence, polarization and magnitude of the EMP, and length of apertures. Based on the transient response, further design of protection can be implemented to suppress the received jitter of voltage pulses.

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable numerical scheme, being proposed to remove stability limitations in conventional FDTD methods. Though the computation efficiency has been improved by ADI-FDTD, significant errors have been observed at large time steps. By compensating truncation errors, a low error ADI-FDTD method in Debye media is proposed based the ER(error reduced)-ADI-FDTD, complete three dimensional equations are derived. Simulation results are anlalyzed and compared with existing methods.

This paper presents unconditionally stable and conformal FDTD schemes which are based on the alternating-direction implicit finite difference time domain (ADI-FDTD) method for accurate modeling of perfectly electric conducting (PEC) objects. The proposed schemes are formulated within the framework of the matrix-vector notation of the finite integration technique (FIT), which allows a systematic and consistent extension of finite difference solution of Maxwell's equations on dual grids. As possible choices of second-order convergent conformal method, we apply the partially filled cell (PFC) and the uniformly stable conformal (USC) schemes for the ADI-FDTD method. The unconditional stability and the rates of convergence of the proposed conformal ADI-FDTD (CADI-FDTD) schemes are verified by means of numerical examples of waveguide problems.

In this letter, an efficient high-order absorbing boundary condition for the alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method is developed. The proposed high-order absorbing boundary condition (ABC) has very high numerical efficiency because it can keep the tri-diagonal matrix form during the ADI iteration. The absorbing performance of the proposed ABC is analyzed theoretically. To verify the performance of the proposed high-order ABC, a rectangular waveguide problem which has very strong dispersion characteristic is analyzed with the ADI-FDTD method. Numerical results show that the proposed high-order ABC has excellent absorbing performance.

An efficient and unconditional stable formulations of the perfectly matched layer (PML) are presented for truncating linear Debye and Lorentz dispersive Finite Difference Time Domain (FDTD) grids. The formulations incorporate the Digital Signal Processing algorithms developed for digital filters into the Alternating Direction Implicit FDTD method. Numerical examples are included to validated the proposed formulations.

In this paper, a 3D alternating-direction implicit finite-difference time-domain (ADI-FDTD) algorithm is used to analyze planar circuits. The source excitation in ADI-FDTD is described and two kinds of absorbing boundary conditions (ABCs) are jointly employed for ADI-FDTD algorithm: the Gedney's uniaxial PML scheme is applied in the propagation direction, and Mur's 1st-order absorbing boundary condition (ABC) is set on the other outer surfaces. Both time-domain waveforms and S-parameters are presented. The numerical simulations of several examples show that the number of iterations with this ADI-FDTD algorithm can be six times less than that with the conventional FDTD without a large loss of accuracy. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 175–179, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20936

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

With the rapid development of Bluetooth wireless communication, it's highlighted now to applying micro-electro-mechanical systems (MEMS) technique in the radio frequency (RF) field to manufacture broadband Bluetooth antennas. The 10 dB bandwidth and efficiency of the micromachined Bluetooth antenna designed in this paper are more than 11% and 68% respectively; the length is less than 1/10 wavelength. The alternating direction implicit finite-difference time-domain (ADI-KDTD) method for a full three-dimensional (3-D) wave presented is used for modeling and analyzing the micromachine antenna for the first time. Numerical simulation results are compared to those using the conventional 3D finite-difference time-domain (FDTD) method. It is more efficient than the conventional 3-D FDTD method in terms of the central processing unit time if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength.

A numerical dispersion optimized leapfrog alternating direction implicit finite-difference time-domain (ADI-FDTD) method is proposed in this paper, where a set of artificial anisotropic parameters is introduced into its implementation. Under such circumstances, its numerical dispersion can be suppressed efficiently. Some numerical experiments are performed and compared with the original leapfrog ADI-FDTD method, it is shown that our proposed method can achieve much higher computational accuracy. Further, such method is adopted for predicting surface current distributions of some 3-D complex objects illuminated by an electromagnetic pulse (EMP), such as a tank and an aircraft, etc., and good agreement is obtained in comparison with commercial software.