Development of an unconditionally stable finite-difference time-domain method for electromagnetic modeling and applications.

摘要

Maxwell's equations, which represent a fundamental relationship between electric and magnetic fields, have been studied for decades. Although the analytical solutions have been given for analyzing many microwave structures, it is difficult to obtain them for predicting field behaviors in complex structures with composite materials. Consequently, numerical techniques have been studied, applied and proven to be effective in both time domain and frequency domain. With the particular desire of obtaining the full wave analysis for the microwave devices in an efficient manner, researchers have been driven into finding novel time domain techniques. The Finite-difference Time-domain (FDTD) method was then developed and has been extensively investigated and employed in solving electromagnetic problems due to its simplicity, effectiveness and flexibility. It has become one of the most popular time-domain methods so far. For the electrically large structures and highly conductive materials, however, the FDTD algorithm requires large computation resources and prohibitively long simulation time owing to its two inherent limits: dispersion errors and Courant Friedrich-Levy (CFL) stability condition. Several FDTD-based algorithms, aiming at removing or alleviating the two constraints, have been recently developed. They include multiresolution time-domain (MRTD) method and pseudospectral time-domain (PSTD) method for reduction of numerical dispersion, and alternating direction implicit FDTD (ADI-FDTD) method for complete removal of CFL condition.; So far, the ADI-FDTD method has been applied only to the Cartesian coordinates system. As well, its exclusive advantages have not been fully explored in solving practical electromagnetic problems. In this thesis, the newly developed three-dimensional ADI-FDTD method in the cylindrical coordinates system is presented for effectively analyzing cylindrical microwave devices, especially body of rotational (BOR) structures.; To further demonstrate the exclusive advantages of the ADI-FDTD method in solving practical electromagnetic problems, two resonant structures with conductive materials have been computed with the proposed method. A modified ADI-FDTD method in cylindrical coordinates system is specifically derived for solving highly conductive materials.; Finally, the ADI-FDTD algorithm is successfully combined with the popular absorbing boundary conditions (ABCs) for simulating open strictures. (Abstract shortened by UMI.)