An approach to multi-resolution in time domain based on the discrete wavelet transform

In this paper, an approach to multiresolution in time domain (MRTD) is presented. Maxwell equations are discretized using finite differences in time and a derivative matrix in space that allows any desired level of spatial resolution. This derivative matrix acts on the coefficients that represent the expansion of the field components. These coefficients are calculated by means of the Discrete Wavelet Transforms (DWT). In this work hard (PEC and PMC) boundary conditions have been introduced into the algorithm using the method of images. This approach is valid for any kind of wavelet functions. Stability and dispersion properties are also investigated. Some numerical results, showing multi-resolution properties are presented.