Explicit stencil computation schemes generated by Poisson's formula for the 2D wave equation
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Bibliographic record
Abstract
Abstract A new approach to building explicit time‐marching stencil computation schemes for the transient two‐dimensional acoustic wave equation is implemented. It is based on using Poisson's formula and its three time level modification combined with polynomial stencil interpolation of the solution at each time‐step and exact integration. The time‐stepping algorithm consists of two explicit stencil computation procedures: a first time‐step procedure incorporating the initial conditions and a two‐step scheme for the second and next time‐steps. Three particular explicit stencil schemes (with 5, 9, and 13 space points) are constructed using this approach. Their stability regions are presented. All of the obtained first time‐step computation expressions are different from those used in conventional finite‐difference methods. Accuracy advantages of the new schemes in comparison with conventional finite‐difference schemes are demonstrated by simulation using an exact benchmark solution.
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Full frame distilled prediction
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 |
Machine scores (provisional)
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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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