On Daubechies wavelet based time domain scheme

The wavelet-Galerkin time domain (WGTD) approach proposed by Cheong et al., (1999), significantly simplified the multi-resolution time domain technique (MRTD) of Krumpholz et al., (1996). In this paper, we provide a rigorous analysis of the WGTD, employing positive sampling functions and their biorthogonal dual. This biorthogonal system has exact interpolation properties and demonstrates superiority over the FDTD in terms of memory and speed. Numerical examples and comparisons to the traditional FDTD results are provided.