Analysis and numerical experiments on the numerical dispersion of two-dimensional ADI-FDTD
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Bibliographic record
Abstract
The numerical dispersion relations in the literature are inconsistent for the alternate-direction-implicit finite-difference time-domain (ADI-FDTD) method. By analysis of the amplification factors, the numerical dispersion relation is rederived and verified with numerical experiments, with good agreement. The inconsistency of the numerical dispersion relation is resolved. It is shown that ADI-FDTD has some fundamental limits. For a given time step size, there is a velocity error even for zero spatial mesh. For a given spatial mesh size, the mesh does not support a numerical wave at certain time step sizes. As the Nyquist sampling limit is approached, the velocity of the wave approaches zero. At about twice the Nyquist limit, the wave does not propagate. Hence, the Nyquist criterion should be respected in choosing the time step size.
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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 | 0.000 | 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) | 0.000 | 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