On exact truncation of backward waves in elastrodynamics

For elastic wave scattering problems in unbounded anisotropic media, the existence of backward waves makes classic truncation techniques fail completely. This paper is concerned with an exact truncation technique for terminating backward elastic waves. We derive a closed form of elastrodynamic Green...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Author: Lu, Wangtao
Format: Article
Language:English
Subjects:
Algorithms
Anisotropic media
Backward waves
Boundary conditions
Elastic anisotropy
Elastic scattering
Elastic waves
Fourier transforms
Mathematical analysis
Tensors
Wave scattering
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Summary:For elastic wave scattering problems in unbounded anisotropic media, the existence of backward waves makes classic truncation techniques fail completely. This paper is concerned with an exact truncation technique for terminating backward elastic waves. We derive a closed form of elastrodynamic Green's tensor based on the method of Fourier transform and design two fundamental principles to ensure its physical correctness. We present a rigorous theory to completely classify the propagation behavior of Green's tensor, thus proving a conjecture posed by Bécache, Fauqueux and Joly (J. Comp. Phys., 188, 2003) regarding a necessary and suffcient condition of the non-existence of backward waves. Using Green's tensor, we propose a new radiation condition to characterize anistropic scattered waves at infinity. This leads to an exact transparent boundary condition (TBC) to truncate the unbounded domain, regardless the existence of backward waves or not. We develop a fast algorithm to evaluate Green's tensor and a high-accuracy scheme to discretize the TBC. A number of experiments are carried out to validate the correctness and efficiency of the new TBC.
ISSN:2331-8422