Qi Wei

TL;DR: This paper aims to propose a wavelet boundary element method (WBEM) to study the three-dimensional elasticity problem and potential problem and illustrates the good convergence, reliability, and flexibility of WBEM by comparison with the traditional BEM and exact solutions.

TL;DR: In this paper , a wavelet-based boundary element method (WBEM) was used to determine the band structures of two-dimensional solid-solid and fluid-fluid phononic crystals.

Abstract: A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

TL;DR: In this paper, a wavelet-based boundary element method is employed to calculate the band structures of two-dimensional phononic crystals, which are composed of square or triangular lattices with scatterers of arbitrary cross sections.