Moving Mesh Methods on Parametric Surfaces
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Many phenomena in the applied and natural sciences occur on surfaces. To solve accurately the corresponding partial differential equations (PDEs), it is often necessary to adapt the mesh, based upon the geometry of the surface, or based upon the behaviour of the PDE solution. Moving mesh methods are particularly efficient strategies in many situations. PDEs explicitly involving the mesh speed, called moving mesh PDEs (MMPDEs), offer a robust technique to adapt the mesh. In this work, we implement, with the C++ finite element library deal.II, a mesh adaptation based on Winslow's adaptation functional. We generalize the moving mesh problem to curved surfaces by deriving appropriate mathematical and finite element formulations. Furthermore, a simple method using surface parameterization is developed and implemented using deal.II. The results, for both fixed and dynamically adapting meshes, demonstrate the effectiveness of the method.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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