A Parallel Meshless Formulation for <formula><tex>$h$</tex> </formula>-<formula formulatype="inline"><tex>$p$</tex></formula> Adaptive Finite Element Analysis
Bibliographic record
Abstract
A novel parallel formulation for meshless adaptive finite element analysis is developed and investigated. The method is based on an integrated interpretation of conventional meshless theory and the generalized irregular-cut formulation for triangles and tetrahedra. The new formulation provides a near orthogonal hierarchal relationship among local basis functions, and supports the virtually unrestricted introduction and refinement of localized modeling degrees of freedom in a discretization. The formulation is intended for h-p adaptive refinements, and is well suited to high-performance parallel and distributed computing implementations. Initial test implementations have been purpose-built to investigate the main issues and performance characteristics of adaptive finite element analysis applications in electromagnetics, for large-scale computations on the CLUMEQ Supercomputer Centre facilities at McGill University, Montreal, QC, Canada. Numerical results based on 1-D, 2-D, and 3-D benchmark analyses verify the correctness of the new formulation and illustrate the potential performance of the implementations.
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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 | 0.000 | 0.001 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".