Stochastic domain decomposition for time dependent adaptive mesh\n generation
Bibliographic record
Abstract
The efficient generation of meshes is an important component in the numerical\nsolution of problems in physics and engineering. Of interest are situations\nwhere global mesh quality and a tight coupling to the solution of the physical\npartial differential equation (PDE) is important. We consider parabolic PDE\nmesh generation and present a method for the construction of adaptive meshes in\ntwo spatial dimensions using stochastic domain decomposition that is suitable\nfor an implementation in a multi- or many-core environment. Methods for mesh\ngeneration on periodic domains are also provided. The mesh generator is coupled\nto a time dependent physical PDE and the system is evolved using an alternating\nsolution procedure. The method uses the stochastic representation of the exact\nsolution of a parabolic linear mesh generator to find the location of an\nadaptive mesh along the (artificial) subdomain interfaces. The deterministic\nevaluation of the mesh over each subdomain can then be obtained completely\nindependently using the probabilistically computed solutions as boundary\nconditions. The parallel performance of this general stochastic domain\ndecomposition approach has previously been shown. We demonstrate the approach\nnumerically for the mesh generation context and compare the mesh obtained with\nthe corresponding single domain mesh using a representative mesh quality\nmeasure.\n
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".