Wavelet-based finite element simulation of guided waves containing harmonics

Abstract

This paper presents a promising numerical scheme for simulation of many harmonics in wave propagation. The wavelet-based adaptive technique eliminates the requirement for a very large number of nodes in finite element method for propagation of such waves. This dynamic adaptive grid selection is based on the fact that very few wavelet coefficients are required to represent a short pulse containing higher harmonics. The method is particularly useful where higher harmonics are ignored due to very high computational cost. In this work, B-spline and Daubechies wavelets-based non-standard (NS) multi-scale operator are applied, and the results are compared with the finite element method.