Multiresolution Daubechies finite wavelet domain method for transient dynamic wave analysis in elastic solids

• Published in: International journal for numerical methods in engineering 2021-12, Vol.122 (23), p.7078-7100
• Main Authors: Nastos, Christos V., Saravanos, Dimitris A.
• Format: Article
• Language: English
• Subjects: Basis functions; Daubechies wavelets; Domains; Elastic analysis; elastic waves; explicit structural dynamics; multiresolution analysis; Numerical methods; Propagation; transient response; Wave propagation; wavelet‐based elements
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6822

The multiresolution capability provided by the family of Daubechies wavelets is exploited to develop a new computational approach, termed as multiresolution finite wavelet domain method for the fast and hierarchical prediction of transient dynamic problems with focus on wave propagation in one‐ and two‐dimensional structural configurations. In the developed method, both scaling and wavelet functions are employed as basis functions for the approximation of displacements in the governing dynamic equations. Because of the orthogonal and the multiresolution properties of Daubechies wavelets, a two‐scale system of mass uncoupled dynamic equations, representing the coarse and the fine spatial wave component solutions is derived. Numerical results concerning wave propagation in one‐ and two‐dimensional elastic structures demonstrate substantial computational gains of the method in comparison with other well‐established numerical methods. Moreover, additional benefits of the involved coarse and fine solutions enabling the analysis and characterization of the resultant wave response are revealed and discussed.