Implementation of Adaptive Gaussian Quadrature for Improved Accuracy of Boundary Element Methods Applied to Three Dimensional Geometries
Bibliographic record
Abstract
Abstract An adaptive Gaussian quadrature method for characterizing flow over three dimensional bodies via a boundary element method using isoparametric quadrilateral elements with non-constant source and dipole strengths has been developed and tested. This method is compared to state-of-the-art methods: flat elements with constant strengths, flat elements with bilinear strengths, and twisted elements with constant dipole strengths. As such, an overview of current boundary element methods is provided. The method developed here for twisted elements with non-constant source and dipole strengths is advantageous in that it both better approximates the actual geometry of the surface and the distribution of the dipole and source strengths. The majority of current methods are lacking at least one of these attributes. The developed method has been validated by comparison to two known analytical solutions: a non-lifting ellipsoid and a Kármán-Trefftz airfoil. The flexible and robust procedure presented here results in improved accuracy of the solution to the Laplace equation around three dimensional bodies.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".