A Non-Uniform Mesh High-Order Finite-Difference Time-Domain Method based on Biorthogonal Interpolating Functions
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Bibliographic record
Abstract
This paper addresses, for the first time, the question of non-uniform meshing within the context of a recently formulated high-order finite-difference technique that employs Deslauriers-Dubuc biorthogonal interpolating basis functions for the expansion of electromagnetic field components in space. To that end, a domain overriding approach is developed and shown to present a very low level of reflections at interfaces between meshes of different densities, enhancing the accuracy and versatility of the Deslauriers-Dubuc scheme (which lends itself to the modeling of complex, inhomogeneous media, unlike earlier similar methods), while providing a generic approach to embedding subgrids within high-order finite-difference meshes.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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.
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