Development of the Three-Dimensional Unconditionally Stable LOD-FDTD Method

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is a promising unconditionally stable scheme that may improve the computational efficiency. However, no general dispersive media were considered in the ADI-FDTD community. The dispersive property, in fact, is important for semiconductor device design at radio-frequency. In this paper, the ADI-FDTD method is applied to complex structures such as on-chip spiral inductor with honeycomb oxide trench, buried layer removal, and radial patterned ground shield. The proposed formula is applicable to linearly dispersive and lossy media. Using this approach, the overall accuracy has been obtained with little computational overhead

A three-dimensional unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD-FDTD) method is presented. Unlike the two-step LOD-FDTD and three-step LOD-FDTD methods, the proposed method has second order temporal accuracy. Hence, it gives less numerical dispersion than the two-step LOD-FDTD and three-step LOD-FDTD methods. It also gives less numerical dispersion than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. Moreover, for every propagation angle θ, it provides very small anisotropy error than the above-mentioned FDTD methods. Effects of the time step and the mesh size on the performance of the proposed method are discussed in detail. In this paper, validation of the stability and the accuracy of the proposed method is done with the help of simulation results. To further show the advantage of the proposed method, performance of the proposed method with artificial coefficients (control parameters) is also discussed in this paper.

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.

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.

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.

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.

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.

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.

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 letter, a circular absorbing boundary using the radial perfectly matched layer (RPML) is investigated for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. A staircase approach is used to approximate the circular boundary so that it is directly compatible with the commonly used Yee's lattice. The proposed RPML boundary is computationally more efficient than the traditional rectangular PML boundary. It was found that more than 20% of the memory and computation time can be saved by using the proposed method.

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.

The intraband term of the graphene electronic model is incorporated into Maxwell equations, and then the locally one-dimensional finite difference time domain (LOD-FDTD) method is applied to simulate graphene devices efficiently. Numerical results of the approach are compared with the explicit FDTD method. At Courant Friedrich Levy number (CFLN) equal to 100, the proposed approach is approximately 60% faster in terms of simulation time and with reasonable accuracy as compared to the FDTD method.