Takefumi Namiki

A new FDTD algorithm based on alternating-direction implicit method

In this paper, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on an alternating-direction implicit method. It is shown that the new algorithm is quite stable both analytically and numerically even when the CFL condition is not satisfied. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than conventional FDTD schemes in terms of computer resources such as central-processing-unit time. Numerical formulations are presented and simulation results are compared to those using the conventional FDTD method.

Investigation of numerical errors of the two-dimensional ADI-FDTD method [for Maxwell's equations solution]

We previously proposed the ADI-FDTD method as a means of solving two-dimensional Maxwells equations. The algorithm used in this method is unconditionally stable, which means the time-step size ran be set arbitrarily when this method is used. The limitation of the time-step size is not dependent on the Courant-Friedrich-Levy (CFL) condition, but on numerical errors such as numerical dispersion. In this paper, we investigate the numerical errors of the method quantitatively and discuss the calculation accuracy and efficiency of the method. We found that a large time-step size results in high numerical dispersion. However, the limit of the time-step size due to numerical dispersion is greater than the CPL limit if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength. In that case, because the large time-step size reduces the number of time-loop iterations, the ADI-FDTD method is more efficient than the conventional FDTD method in terms of computer resources such as central processing unit time.

A new FDTD algorithm free from the CFL condition restraint for a 2D-TE wave

A new finite-difference time-domain algorithm, which is based on an alternating direction implicit method, is proposed in order to eliminate the Courant-Friedrich-Levy condition restraint. It is shown that the new algorithm is quite stable numerically even when the CFL condition is not satisfied. Therefore, if the cell size in the computational domain is locally much smaller than the wavelength, this new algorithm is more efficient than conventional FDTD schemes in terms of computer resources such as central processing unit (CPU) time.

Numerical simulation of microstrip resonators and filters using the ADI-FDTD method

In this paper, we derived the characteristics of typical and practical microstrip components such as microstrip linear resonators and microstrip low-pass filters using the alternating-direction-implicit-finite-difference-time-domain (ADI-FDTD) method to examine the calculation accuracy and efficiency of the method. The resonators and the filters included very narrow gaps and strips, respectively. In this case, very fine cells must be applied there for the finite-difference time-domain (FDTD) modeling. In the conventional FDTD method, fine cells cause a reduction of the time-step size because of the Courant-Friedrich-Levy (CFL) stability condition, which results in an increase in calculation time. In the ADI-FDTD method, on the other hand, a larger time-step size than the CFL stability condition limitation could be set. We compared the results of the ADI-FDTD method for various time-step sizes with the results of the conventional FDTD method and measured data.

Improving radiation-pattern distortion of a patch antenna having a finite ground plane

This paper presents a very useful and yet simple method of improving the radiation-pattern distortion of a patch antenna having a finite ground plane. The improvement can be achieved by cutting out the edges of the finite ground plane. This produces a phase shift between the induced equivalent magnetic currents on the edges, thereby causing cancellation in the diffracted fields. We numerically and experimentally examined the effects for some typical patch antennas and confirmed that the ripples in the copolar E plane pattern could be eliminated by using this approach.

Numerical simulation using ADI-FDTD method to estimate shielding effectiveness of thin conductive enclosures

Numerical simulations were run using the alternating-direction implicit-finite-difference time-domain (ADI-FDTD) method to calculate the shielding effectiveness of various enclosures. The enclosures were composed of very thin conductive sheets, which are generally fabricated using conductive paints or electroless plating techniques on plastic surfaces. In this case, very fine cells must be used for finite-difference time-domain (FDTD) modeling. In the conventional FDTD method, fine cells reduce the time-step size because of the Courant-Friedrich-Levy (CFL) stability condition, which results in an increase in computational effort, such as the central processing unit (CPU) time. In the ADT-FDTD method, on the other hand, a larger time-step size than allowed by the CFL stability condition limitation can be set because the algorithm of this method is unconditionally stable. Consequently, an increase in computational efforts caused by fine cells can be prevented. The results from the ADI-FDTD method were compared with results from the conventional FDTD method, analytical solutions, and experimental data. These results clearly agree quite well, and the required CPU time for the ADI-FDTD method can be much shorter than that for the FDTD method.

Accuracy improvement technique applied to non-uniform FDTD cells using high-order implicit scheme

The finite-difference time-domain (FDTD) method is performed on discrete rectangular cells in the computational domain, and non-uniform cells are often used to save computational costs. Non-uniform cells increase the truncation error at the boundary of two domains whose cell sizes differ. We apply a high-order implicit scheme at the boundary to reduce this error. Numerical formulations and error criteria of the scheme are described and evaluated in practical applications. Compared with the conventional FDTD method, the new technique is more accurate.

A stable FDTD subgridding method for both spatial and temporal spaces

The proposed FDTD subgridding method is stable in both spatial and temporal spaces. Late-time instability has been resolved by separating the space and time interpolation interfaces from conventional collocated to same position. Numerical experiments conducted in 2D of 10 million time steps have no instability problem after a minimum gap distance for various refinement factors. Compare to existing subgridding methods the new method is not restricted to a single refinement factor and need no special treatment at material interfaces. This should open the FDTD subgridding method to more applications.

Unconditionally stable FDTD algorithm for solving three-dimensional Maxwell's equations

We previously introduced an unconditionally stable FDTD algorithm for a two-dimensional TE wave. This algorithm is based on the alternating-direction implicit (ADI) method, so we have called this new algorithm the ADI-FDTD method. We analytically and numerically verified that the algorithm of this method is free from the Courant-Friedrich-Levy condition restraint. In this paper, we extend this approach to a full three-dimensional wave. Numerical formulations are presented and simulation results are compared to those using the conventional FDTD method.

Numerical simulation of antennas using three-dimensional finite-difference time-domain method

The paper presents numerical simulations of various antennas using the three dimensional finite difference time domain (FDTD) method. The FDTD code uses the perfectly matched layer absorbing boundary condition (PML-ABC) and a time domain near to far field transformation function. The method is shown to be an efficient tool for modeling complicated antenna structures. The calculation results are compared with the measured data and shown to be in good agreement.