A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media
Abstract
Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded lossless anisotropic medium. The formulation is based on a second-order approach that has the advantages of, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. Specifically, our formulation uses three second-order equations of the displacement field and nine auxiliary equations, along with the three time histories of the displacement field. The properties of the PML, which are controlled by a complex two-parameter stretch function, are such that it acts as near perfect absorber. Using finite element method (FEM) 3D numerical results are presented for a highly anisotropic medium. An extension of the formulation to the particular case of a Kelvin-Vogit viscoelastic medium is also presented.
- Publication:
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Acoustical Society of America Journal
- Pub Date:
- October 2016
- DOI:
- 10.1121/1.4970329
- arXiv:
- arXiv:1607.06478
- Bibcode:
- 2016ASAJ..140.3261A
- Keywords:
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- Mathematics - Numerical Analysis;
- Physics - Computational Physics
- E-Print:
- doi:10.1121/1.4970329