A Stable and Efficient Direct Time Integration of the Vector Wave Equation in the Finite-Element Time-Domain Method for Dispersive Media
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Bibliographic record
Abstract
The finite-element time-domain (FETD) solution of the vector wave equation (VWE) is directly extended to doubly dispersive media using the bilinear transform approach. The proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional-based approaches. In addition, it can be implemented in a very straightforward and efficient manner. A stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case. However, in order to avoid the well-known late-time instabilities that arise in this formulation, an alternative formulation is considered and extended to the dispersive case with the same approach. Several numerical examples are simulated to verify the validity and accuracy of the proposed formulations. The late-time stability of the alternative formulation is tested through a numerical example with 20 million time steps. The solution is completely free from late-time growth.
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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