Speed comparison of solution methods for the obstacle problem
Bibliographic record
Abstract
Obstacle problems can be solved iteratively.Several solution methods are implemented and their speeds are compared.Speed is measured both in terms of the number of iterations required to converge and the average CPU time needed for one iteration for each method.The implementation is done using MATLAB for problems in one and two dimensions.The Euler iterative method requires a large number of iterations to converge to the solution.The semismooth Newton's method (SSNM) requires fewer iterations.Even fewer iterations are achieved with the combined method, which alternates between several Euler steps and one SSNM step.The behavior of the three different solution methods is compared extensively, and the combined method is declared as the best. AbrgLes problmes de l'obstacle peuvent tre rsolus itrativement.Plusieurs mthodes numriques sont dveloppes et leurs vitesses sont compares.La vitesse d'une mthode est dtermine en considrant le nombre d'itrations ncessaires pour converger ainsi que le temps moyen requis par le processeur pour une seule itration.La ralisation est faite avec MATLAB en une et deux dimensions.La mthode itrative d'Euler exige un grand nombre d'itrations pour converger vers la solution.La mthode de Newton semismooth (MNSS) exige moins d'itrations.Les deux mthodes sont combines en alternant quelques pas d'Euler avec un pas de la MNSS.Encore moins d'itrations sont ncessaires pour cette mthode de combinaison.La performance des trois mthodes est compare et la mthode de combinaison est dclare gagnante.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".