Abstract
This paper discusses the wavelet-based Finite Difference Time Domain (FDTD) method and a tunable high resolution estimator 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), some disadvantages, such as time consuming and the numerical instability of FDTD iterations are encountered. Moreover, good frequency estimation can only be ensured by the postprocessing of sufficiently long time series. In this paper, a wavelet-based FDTD and a tunable high resolution estimator based on a bank of filters are proposed to overcome these difficulties. Numerical results for twodimensional phononic crystal show that the wavelet-based FDTD method improves the efficiency of the time stepping algorithm and the stability of iterations, and tunable high resolution estimator shows the advantages over the FFT-based spectral estimation.
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