A COST/BENEFIT ANALYSIS OF SIMPLICIAL MESH IMPROVEMENT TECHNIQUES AS MEASURED BY SOLUTION EFFICIENCY
Bibliographic record
Abstract
The quality of unstructured meshes has long been known to affect both the efficiency and the accuracy of the numerical solution of application problems. Mesh quality can often be improved through the use of algorithms based on local reconnection schemes, node smoothing, and adaptive refinement or coarsening. These methods typically incur a significant cost, and in this paper, we provide an analysis of the tradeoffs associated with the cost of mesh improvement in terms of solution efficiency. We first consider simple finite element applications and show the effect of increasing the number of poor quality elements in the mesh and decreasing their quality on the solution time of a number of different solvers. These simple application problems are theoretically well-understood, and we show the relationship between the quality of the mesh and the eigenvalue spectrum of the resulting linear system. We then consider realistic finite element and finite volume application problems, and show that the cost of mesh improvement is significantly less than the cost of solving the problem on a poorer quality mesh.
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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 | 0.006 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".