Stability condition and numerical dispersion of wavelet Galerkin scheme-based precise integration time domain method

In this paper, the stability condition and the numerical dispersion relation of the wavelet Galerkin scheme-based precise integration time domain (WG-PITD) method are derived in a Hilbert space. The Daubechies scaling functions with high order are used as the basis functions in the spatial discretization of the WG-PITD method. It is found that the time step size of the WG-PITD method can be of a value much larger than the Courant-Friedrich-Levy (CFL) stability limitation of the finite difference time domain (FDTD) method. The Daubechies scaling functions with higher order always give smaller numerical dispersion error in the WG-PITD method.