

A Wavelet-Based Spectral Finite Element Method for Simulating Elastic Wave Propagation
Abstract
In the present paper, a novel formulation of the wavelet-based finite element method (WSFEM) is proposed and applied to the in-plane wave equations in orthotropic plate structures. By computing the exact values of the connection coefficients of Daubechies compactly supported wavelets over a finite interval, the wavelet-Galerkin method is employed. Subsequently, the elastodynamic equations are decoupled with respect to the transformation parameter. Contrary to more conventional transformed domain methods which have difficulties in handling relatively complex geometries, the response in the transformed (wavelet) domain is fully discretized in analogy with FEM. However, unlike the conventional FEM, the basis functions in the proposed WSFEM are functions of the wavenumbers in the transformed domain. It is shown in the paper that the proposed WSFEM converges faster than FEM with linear or quadratic basis functions with substantially fewer number of time sampling points. Since the present approach allows for solving the transformed governing equations for each wavelet point separately, the method is inherently suitable for parallel computation. In addition, the temporal discretization is not influenced by the FE mesh.