Dispersion Analysis of Multiscale Wavelet Finite Element for 2D Elastic Wave Propagation
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
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.
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Data Availability Statement
All data used during the study appear in the published article, while the codes used during the study are available from the corresponding author by request.
Acknowledgments
The authors are grateful for the financial support from the National Key Research and Development Program of China (Project No. 2017YFC0703410), and the National Natural Science Foundation of China (NSFC) under Grant No. 51778104.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 4 • April 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 26, 2018
Accepted: Nov 6, 2019
Published online: Feb 13, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 13, 2020
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