Abdullah Y. Oztoprak

An Unconditionally Stable Split-Step FDTD Method for Low Anisotropy

Split-step unconditionally stable finite-difference time-domain (FDTD) methods have higher dispersion and anisotropic errors for large stability factors. A new split-step method with four sub-steps is introduced and shown to have much lower anisotropy compared with the well known alternating direction implicit finite-difference time-domain (ADI-FDTD) and other known split step methods. Another important aspect of the new method is that for each space step value there is a stability factor value that the numerical propagation phase velocity is isotropic.

Optimized exponential operator coefficients for symplectic FDTD method

A new symplectic finite difference time domain scheme is introduced. The scheme uses fourth-order finite differencing for space and a symplectic scheme with a propagator of exponential differential operators for time. The coefficients of the exponential operators are obtained by optimizing the higher order terms of the growth factor for high Courant stability limit as well as by using the Taylors series expansion of the exponential operator for up to the second-order term. When the Taylors series expansion of the exponential operator is considered the new scheme is second-order in time, but the dispersion performance of the scheme is similar to the performance of the fourth-order symplectic schemes previously reported. The stability performance is shown to be better, and as the new scheme uses smaller number of exponential operators it also reduces the computational time. One other advantage of this scheme is that it is flexible in the choice of the coefficients, which allows the coefficients to be chosen according to performance requirements.

Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwells equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.

Higher Stability Limits for the Symplectic FDTD Method by Making Use of Chebyshev Polynomials

A new scheme is introduced for obtaining higher stability performance for the symplectic finite-difference time-domain (FDTD) method. Both the stability limit and the numerical dispersion of the symplectic FDTD are determined by a function zeta. It is shown that when the zeta function is a Chebyshev polynomial the stability limit is linearly proportional to the number of the exponential operators. Thus, the stability limit can be increased as much as possible at the cost of increased number of operators. For example, the stability limit of the four-exponential operator scheme is 0.989 and of the eight-exponential operator scheme it is 1.979 for fourth-order space discretization in three dimensions, which is almost three times the stability limit of previously published symplectic FDTD schemes with a similar number of operators. This study also shows that the numerical dispersion errors for this new scheme are less than those of the previously reported symplectic FDTD schemes

A method for minimizing the phase errors of Rotman lenses

A method is introduced for determining the feed curves of Rotman lenses such that the phase errors are minimized. The method ensures that there are at least three zero phase error points on the radiating array for each off focal beam position. The results of a path length error study show that there is a very significant drop in the level of the maximum phase errors (in the order of about 4:1) compared with the commonly used circular and elliptical feed curves.

Parallel Implementation of the Wave-Equation Finite-Difference Time-Domain Method Using the Message Passing Interface

The parallel implementation of the Wave Equation Finite Difference Time Domain (WE-FDTD) method, using the Message Passing Interface system, is presented. The WE-FDTD computational domain is divided into subdomains using one-dimensional topology. Numerical simulations have been carried out for a line current source radiating in two-dimensional domains of different sizes and performed on a network of PCs interconnected with Ethernet. It has been observed that, for large computational domains, the parallel implementation of the WE-FDTD method provides a significant reduction in the computation time, when compared with the parallel implementation of the conventional FDTD algorithm.

Estimating the phase centre of two dimensional radiators

A method has been introduced for determining the phase center of two dimensional radiators. This method involves the determination of the phase errors against the angle at the far field of the radiator with reference to the center of the aperture of the radiator. The phase center is than estimated by equating the phases at the broadside and at a chosen angle. The results show that there is almost no phase error over the range of angles of interest for the estimated phase center at the design frequency. The position of the phase center does not vary with the distance from the radiator, which means that there are no phase errors as the distance from the radiator varies. Although there are some phase errors as the frequency varies, these errors are not significant over a wide band of frequencies.

Zero error split step FDTD method for narrow band applications

It has recently been reported that the four split step finite difference time domain (4 SS FDTD) method is isotropic at a certain stability factor for each space step value. It is also known that the average value of the numerical phase velocity of FDTD methods can be corrected for given stability factor and space step value. In this paper polynomial expressions are obtained for the stability factor values giving zero numerical phase velocity anisotropic error and zero error average numerical phase velocity. These polynomial expressions are included in the 4 SS FDTD codes, so that once space value is chosen from simulation considerations the stability factor (or the time step) and the numerical phase velocity correction factor is obtained directly. A performance study of the method show that zero error isotropic numerical phase velocity can be obtained at space step values as large as five cells per wavelength. The method is narrowband for large space step values.

Errata to "Z-transform implementation of the perfectly matched layer for truncating fdtd domains"

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwells equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.