Eikonal equation‐based front propagation for arbitrary complex configurations
Bibliographic record
Abstract
Abstract This paper presents a front propagation method using the Eikonal equation, ∇ϕ ⋅ ∇ϕ = 1, in which, ϕ represents the smallest Euclidean distance field to the front to be propagated. The offset capturing approach consists in first calculating the ϕ field over a uniform Cartesian grid fully covering the front to be propagated, and then constructing the iso‐ϕ curves or surfaces as the propagated result. The calculation of ϕ uses a 3D numerical scheme, the Fast Sweeping Scheme . Validation for accuracy of the method is presented using academic test cases. A real 3D industry application, draft tube with two piers, is successfully propagated and demonstrated using special boundary conditions to cope with inlet and outlet planes during front propagtion. This application involves the propagation of a front that exhibits both concave and convex shape regions, sharp corners, and local tangent plane surface discontinuities as well as a multi‐connected domain. Copyright © 2007 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".