Analysis of the dispersion properties of the multiresolution time-domain (MRTD) scheme

A new time-domain scheme for numerically solving Maxwell's equations, termed the multiresolution time-domain (MRTD) method was proposed by Krumpholz and Katehi (see IEEE Microwave Guided Wave Lett., vol.5, p.382-4, 1995, and IEEE Trans. Microwave Theory Tech., vol.44, p.555-71, 1996). They claimed computer savings of two orders of magnitude with respect to memory and one order of magnitude with respect to time over the classic Yee finite-difference time-domain (FDTD) scheme. In this paper, attention is given to the frequencies which are sampled on the order of 10 or 20 points per wavelength since such sampling would typically be present in problems involving broad-band signals. Results show that the MRTD scheme using the cubic spline Battle-Lemarie scaling functions may have worse dispersion properties than the classic second-order Yee algorithm for certain resolutions and choices of Courant number.