| The finite difference time domain (FDTD) method is a numerical method for modeling complicated electromagnetic structures. It has been used widely due to its robustness, programming simplicity and flexibility. However, this technique has the drawback of large computational expenditure, especially when dealing with narrowband signals. The main reason is that due to numerical dispersion, the marching time step has to be set small relative to the highest frequency, although useful envelope information occupies only a small bandwidth around the center or high carrier frequencies. To circumvent this problem, the concept of complex envelope (CE) was recently adapted into the FDTD method. By making use of the complex envelope representation of a narrowband signal, the high carrier frequency is absorbed into the field equations as a known quantity. Consequently, only the signal envelopes become the variants to be sampled and computed.;By following the same procedure in formulating the CE-FDTD method, an unconditionally stable CE ADI-FDTD method is developed. The theoretical proof of the unconditional stability of CE ADI-FDTD method is given and a comprehensive analysis of the numerical dispersion is presented for a three-dimensional case. The impacts of propagation directions, ratio of carrier to envelope frequencies, temporal step size, and spatial step size on the dispersion errors are assessed. Furthermore, to validate the exclusive advantages of the CE ADI-FDTD method in solving practical electromagnetic problems, a planar waveguide and a cavity resonator are solved. The accuracy and efficiency of the proposed CE ADI-FDTD method are then demonstrated and compared with both the conventional FDTD method and the ADI-FDTD method.;It is concluded that, in comparison with the conventional FDTD method and ADI-FDTD method, the CE ADI-FDTD method could efficiently reduce the computational burden, especially in solving bandwidth limited responses.;Investigations into the stability and numerical behaviors of the complex envelope technology are presented in this thesis. They show that the CE FDTD method offers little improvement in accuracy or efficiency over the conventional FDTD method. Therefore, in searching for a better CE-type FDTD method, attention is turned to the recently developed, unconditionally stable ADI-FDTD scheme. |
