Wavelets constructed from spectral domain asymptotic tails of Green's functions

The boundary element method (BEM) is a powerful numerical technique for obtaining approximate solutions in surface acoustic wave (SAW) devices. The "impedance" matrices arising in the BEM applications are typically dense. This property is a serious bottleneck in most applications. Wavelets have been proposed to remedy this shortcoming. However, much remains to be achieved in constructing problem-specific wavelets, which would guarantee the desired degree of sparseness. In this work we generalize our previous ideas and construct scaling functions and wavelets based on the far-field asymptotic tails of the SAW and bulk acoustic wave (BAW) Green's functions in spectral domain. The utilized asymptotic terms correspond to the quasi-static near-field expansion terms of the Green's functions. The resulting wavelets turn out to be B-spline wavelets, and thus, satisfy the criteria of the multiresolution analysis upon construction.