中文摘要：

将双正交小波系统和谱元法的思想结合得到一般有界区域中的双正交小波元,将小波元的边界适应性推广到一阶微分的情形,通过匹配得到严格满足边界条件的小波基函数;基于小波元发展一种一维声子晶体能带计算方法.该方法利用声子晶体本身的结构特点,兼顾小波在数值分析中的优势和边界条件的满足,与周期小波法相比,具有更高的计算精度和计算效率.

英文摘要：

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.