Dispersion Analysis of Multiscale Wavelet Finite Element for 2D Elastic Wave Propagation

Abstract

Recently, the wavelet finite element has been introduced to solve wave propagation problems because of its outstanding compact support, multiscale, and multiresolution characteristics. In this research, the accuracy of a multiscale wavelet element using B-spline wavelet on interval (BSWI) for two-dimensional (2D) elastic wave propagation was theoretically studied through dispersion analysis. The Rayleigh quotient technique was introduced to overcome the difficulties caused by the wavelet element with large internal nodes. The numerical dispersion curves of different wave types (P- and S-waves) for different BSWI elements were provided, and the phase errors and numerical anisotropy were discussed. The effects of material parameters and element distortions on the numerical dispersion were elucidated. The BSWI element and other high-order finite elements were compared. The BSWI element of order four and scale three can almost completely suppress the numerical dispersion and anisotropy when no less than five nodes exist per wavelength. Element distortions can severely aggravate numerical dispersion and anisotropy, but the accuracy can be significantly improved with a local lifting scheme without altering the initial mesh and polynomial order.