Efficient Contouring on Unstructured Meshes for Partial Differential Equations
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Bibliographic record
Abstract
We introduce three fast contouring algorithms for visualizing the solution of partial differential equations based on the PCI (pure cubic interpolant). The PCI is a particular piecewise bicubic polynomial interpolant defined over an unstructured mesh. Unlike standard contouring approaches, our contouring algorithms do not need a fine-structured approximation and work efficiently with the original scattered data. The basic idea is to first identify the intersection points between contour curves and the sides of each triangle and then draw smooth contour curves connecting these points. We compare these contouring algorithms with the built-in Matlab contour procedure and other contouring algorithms. We demonstrate that our algorithms are both more accurate and faster than the others.
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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)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it