A compact representation of the Green function is proposed by applying the discrete wavelet concept in the k-domain, which can be used for the acceleration of scattered field calculations in integral equation methods. A mathematical expression of the Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

In numerical simulations of microwave structures using the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, the time marching scheme comprises two sub-iterations, where different updating schemes for evaluating E and H fields at each sub-iteration can be adopted. In this paper, the E-field implicit-updating (EFIU) and H-field implicit-updating (HFIU) schemes are compared with each other especially with regard to the implementation of local boundary conditions.

To make the best use of the known characteristics of the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method such as unconditional stability and modeling accuracy, an efficient time domain solution with variable time-step size is proposed. Numerical results show that a time-step size for a given mesh size can be increased preserving a desired numerical accuracy over frequencies of interest.