Investigation of boundary algorithms for multiresolution analysis

An investigation on the multiresolution time-domain (MRTD) method utilizing different wavelet levels in one mesh is presented. Contrary to adaptive thresholding techniques, only a rigid addition of higher order wavelets in certain critical cells is considered. Their effect is discussed analytically and verified by simulations of plain and dielectrically filled cavities with Daubechiesʹ and Battle-Lemarie orthogonal, as well as Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelets, showing their insufficiency unless used as a full set of expansion. It is pointed out that improvements cannot be expected from these fixed mesh refinements. Furthermore, an advanced treatment concerning thin metallization layers in CDF algorithms is presented, leading to a reduction in cell number by a factor of three per space dimension compared to conventional finite difference time domain (FDTD), but limited to very special structures with infinitely thin irises. All MRTD results are compared to those of conventional FDTD approaches.