The Plane Wave Methods for the Time-Harmonic Elastic Wave Problems with the Complex Valued Coefficients

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.

Author Details

Long Yuan

Shuai Xi

Binlin Zhang