The Plane Wave Methods for the Time-Harmonic Elastic Wave Problems with the Complex Valued Coefficients
Year: 2021
Author: Long Yuan, Shuai Xi, Binlin Zhang
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1169–1202
Abstract
In this paper the plane wave methods are discussed for solving the time-harmonic elastic wave propagation problems with the complex valued coefficients in two and three space dimensions. The plane wave least-squares method and the ultra-weak variational formulation are developed for the elastic wave propagation. The error estimates of the approximation solutions generated by the PWLS method are derived. Moreover, Combined with local spectral elements, the plane wave methods are generalized to solve the nonhomogeneous elastic wave problems. Numerical results verify the validity of the theoretical results and indicate that the resulting approximate solution generated by the PWLS method is generally more accurate than that generated by a new variant of the ultra-weak variational formulation method when the Lamé constants $\lambda$ and $\mu$ are complex valued.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0350
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1169–1202
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Elastic waves nonhomogeneous plane wave least-squares ultra-weak variational formulation plane wave basis functions error estimates local spectral elements preconditioner.