Wavelet Element Method for Band Structures of Phononic Crystals

A wavelet element method is developed to compute band structures of phononic crystals. It is based on combining biorthogonal wavelet systems with philosophy Of spectral element method. Biorthogonal spline wavelets on interval with boundary adaption are constructed. Boundary adaption of wavelet element is extended to first-order derivatives, due to which construction of basis functions that satisfy boundary conditions exactly is possible. The method takes advantage of structural features of phononic crystals and boundary conditions are satisfied exactly. Better accuracy and higher efficiency are obtained.