A Time Domain Moment Method Based on Daubechies Wavelet Expansions

A novel time domain simulation approach for analyzing real three-dimensional (3-D) microwave structures is presented. The electromagnetic fields of the structure under investigation are expanded into a hierarchical system of Daubechies wavelets and scaling functions as basis functions for all three dimensions leading to a stable, multiscale algorithm. By neglecting small wavelet coefficients and thereby reducing the computational expense, this method is equivalent to a finite difference in time domain scheme with a time dynamic time and space adaptive grid. A brief overview of the main ideas and advantages of this new method as well as the results of a numerical example are given.