Towards the development of unconditionally stable time-domain meshless numerical methods
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Bibliographic record
Abstract
Meshless methods have recently emerged as robust numerical techniques for electromagnetic modeling in time domain. In those methods, a problem domain is represented by scattered spatial nodes instead of numerical meshes, thus the conformal modeling of boundaries and solution refinements can be conveniently achieved. However, the CFL-like numerical stability condition still exists with these meshless methods, which prevents the methods being efficiently applied for general electromagnetic simulations. To overcome the problem, in this paper, we propose the unconditionally stable mesheless methods by incorporating two efficiency-improved implicit schemes, namely the leapfrog alternating-direction-implicit (ADI) and the locally one-dimensional scheme (LOD) schemes, into the radial point interpolation mesheless method (RPIM). The proposed methods are numerically verified for their unconditional stability, and are assessed for their numerical accuracy and efficiency. In comparisons with the conventional RPIM, computational cost can be saved by up to 80% with little sacrifice of accuracy.
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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) | 0.001 | 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 it