Singular Tetrahedral Finite Elements for Vector Electromagnetics
Why this work is in the frame
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Bibliographic record
Abstract
The electromagnetic fields at reentrant edges made of conductor are generally singular and the polynomial basis functions used in traditional finite elements do not model the fields well in these regions. Two new tetrahedral elements are introduced with basis functions that incorporate the known asymptotic variation of the fields with distance from the edge. The basis is split into gradient and rotational parts. Additional vertex functions can be added to improve the conditioning of the global matrix system that arises in the time-harmonic case. Results are presented for the scattering parameters of a number of waveguide discontinuities. The new elements reduce the error considerably compared to the Whitney element, and generally outperform the second-order edge element, even though that has more degrees of freedom
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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) | 0.000 | 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 it