Improved Computational Efficiency of Nearest-Nodes Finite Element Method (NN-FEM)
Bibliographic record
Abstract
The recently developed nearest-nodes finite element method (NN-FEM) has a number of advantages over the conventional finite element method (FEM). The most attractive one is that its performance is nearly not affected by element distortion. However, low computational efficiency of NN-FEM is a major concern, as in the original NN-FEM a local problem has to be solved at each quadrature point to construct shape functions there. In this paper, a new strategy is introduced in NN-FEM for constructing shape functions aiming at improving its computational efficiency. The strategy is, for regular-shape elements, shape functions are constructed at the element center and the obtained shape functions are used at all quadrature points in the element; only for severely distorted elements, shape functions are constructed separately at each quadrature point. Numerical results show that computational efficiency of the NN-FEM can be significantly improved with the above strategy, while other performance of the method is not affected.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".