Wavelet-based dual reciprocity BEM for band-structure calculations of 3D fluid/fluid and solid/solid phononic crystals

The boundary element method (BEM) is presented to calculate the band-structure of three-dimensional fluid/ fluid and solid/solid phononic crystals first time. The frequency-independent fundamental solutions are used as weight functions for deriving integral equations in a unit cell, which can avoid the related nonlinear eigenvalue problems. The dual reciprocity method is employed to handle the domain integral terms, thereby achieving dimensionality reduction. To overcome the drawback of dense matrices in BEM, the boundary physical fields are approximated by using the tensor product B-spline wavelet on the interval and wavelet coefficients. Small entries in system matrices, which are yielded by the vanishing moment property of wavelets, are dropped through the truncation technique. By combining Bloch's theorem and interface continuity conditions, we acquire the generalized eigenvalue equations of depending on an angular frequency. The band-structure can be determined by looping through Bloch wave vectors of interest and solving the eigenvalue equations. Comparing to the finite element method, the present method holds a decided advantage in computational accuracy and efficiency. The sparse system matrices obtained using the truncation technique not only reduce the memory requirements, but also have little impact on the required results.