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.
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 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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.005 | 0.006 |
| Meta-epidemiology (broad) | 0.006 | 0.004 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.004 | 0.000 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.001 | 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; both teacher heads agree on what is shown here.
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".