Fundamental research on multiresolution time domain scheme and its applications

In this paper, we have made fundamental investigation on a generalized mult iresolution time domain (MRTD) scheme on the basis of the cubic spline Batt le-Lemarie scaling and high-level resolution wavelet function expansions fo r electromagnetic applications. Focusing on a one-dimensional electromagnet ic plane wave propagation problem, we summarize generalized orthogonal and semiorthogonal relations used for deriving MRTD updating equations. In this research, we employ high-level wavelets only in the extended discontinuity subregions where electromagnetic fields vary dramatically, while utilizing a scaling function in the entire computational region. It is found that th e computed data is in good agreement with the analytic results and the fini te difference time domain (FDTD) solutions for all cases investigated.