Wavelet-based FDTD and high resolution spectral estimation for calculation of band structures in two-dimensional phononic crystals

This paper discusses the wavelet-based Finite Difference Time Domain (FDTD) method and high resolution spectral estimation with a specific problem of sound wave propagation through phononic crystals. If the band structures of a phononic crystal are calculated by the traditional FDTD method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome the difficulty. Numerical simulation results for two-dimensional phononic crystal show that, the wavelet-based FDTD method improves the efficiency of the time stepping algorithm, and high resolution spectral estimation shows the advantages over the classic FFT-based postprocessing.