Novel unconditionally stable finite-difference time-domain method for electromagnetic and microwave modeling

Computational electromagnetics has been an important research area because its capability and flexibility to accurately model and simulate what is really occurring in an actual electrical and electronic circuit and system. In particular, the demands for efficient analysis of the high-frequency broadband structures have driven the research into the application of time domain techniques. As a result, the finite-difference time-domain (FDTD) method, one of the most popular time domain techniques, has been widely studied and applied in solving electromagnetic problems. Its capability of handling electrically large or high-Q structure problems is, however, limited by the requirements of large computation memory and time. Such requirements are due to the numerical dispersion errors and the Courant-Friedrich-Levy (CFL) stability condition. Consequently, a way to improve the computational efficiency would be to remove or alleviate the two constraints. Most of the recent research efforts so far have been focused on developing low-dispersion schemes such as multiresolution time-domain (MRTD) method and pseudospectral time-domain (PSTD) method to lower computation memory requirement.; In this thesis a new direction is opened in improving the FDTD computation efficiency; i.e. the removal of the CFL stability condition. The principle of alternating direction implicit (ADI) technique that has been used to solve parabolic differential equations is applied. However, unlike the conventional ADI algorithms, a modified ADI technique is developed. The alternation is performed in the mixed coordinates each time step rather than in each coordinate each time step. Consequently, in the three-dimensional case, only two alternations in solution marching are required. Therefore, the CFL stability constraint is completely removed in a FDTD method based on the modified ADI technique. The FDTD time step is no longer restricted by the CFL stability condition but by the modeling accuracy of the FDTD algorithm because of the mixed ADI and the FDTD. The new scheme is named ADI-FDTD.; Theoretical proof of the unconditional stability of ADI-FDTD scheme is given and numerical results are presented to demonstrate the effectiveness and efficiency of the proposed method. It is found that the number of iterations with the proposed ADI-FDTD can be at least four times less than that with the conventional FDTD at the same numerical accuracy. As a result, FDTD iteration number and CPU time are reduced.