A Stable 3-D FDTD Method with Multiple Embedded Reduced-Order Models
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Bibliographic record
Abstract
The finite-difference time-domain (FDTD) method has been widely used for its versatility in solving electromagnetic problems. However, the computational efficiency of FDTD can be significantly reduced in subgridding schemes, where a locally refined grid is adopted in the spatial domain. An emerging approach to accelerate FDTD subgridding is model order reduction (MOR), which can be used to compress the update equations of the refined regions. However, reduced-order models can easily introduce instability when embedded into an FDTD grid. In this paper, we propose a systematic strategy to couple multiple reduced models to a 3-D FDTD grid with guaranteed stability under the Courant-Friedrichs-Lewy (CFL) limit of the fine grid. Furthermore, the CFL limit of the entire scheme can be extended with a perturbation of the reduced model coefficients, which can further improve computational efficiency. A numerical example with two reduced-order models indicates the potential of the proposed algorithm.
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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 | 0.000 | 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) | 0.002 | 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