A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media
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Bibliographic record
Abstract
Perfectly matched layers (PML) are a well-developed method for simulating wave propagation in unbounded media enabling the use of a reduced computational domain without having to worry about spurious boundary reflections. Using this approach, a compact three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded general anisotropic medium. The formulation is based on a second-order approach that has the advantages of well-posedness, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. However, many auxiliary variables are usually need to described second-order PML formulations. The problem becomes more complex for the 3D case modeling which would explain the dearth of compact second-order formulations in 3D. Using finite element method (FEM), 3D numerical results are presented to demonstrate the applicability of our formulation, including a highly anisotropic medium example. Extension of the PML formulation to model the case of a Kelvin-Voigt viscoelastic medium is also provided. In addition, we will present the extension of this formulation to model the transient wave propagation in an unbounded fluid-solid 3D medium in a similar way to that presented by the authors (JASA, 2016) for the 2D case.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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