Optimized finite-difference time-domain methods based on the (2,4) stencil
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Bibliographic record
Abstract
The higher order (2,4) scheme optimized in terms of Taylor series in the finite-difference time-domain method is often used to reduce numerical dispersion and anisotropy. This paper investigates optimization of the numerical dispersion behavior for a square Yee mesh based on the (2,4) computational stencil. It is shown that, for one designated frequency, numerical dispersion can be eliminated for some directions of travel, such as the coordinate axes or the diagonals, or numerical anisotropy can be eliminated entirely, resulting in a constant "residual" numerical dispersion. Using a coefficient-modification technique, the residual numerical dispersion can then be completely eliminated at that frequency, or for a wide-band signal, the numerical dispersion error and the averaged-accumulated phase error can be minimized. The stability of the method is analyzed, the numerical dispersion relation is given and validated using numerical experiments, and the relative rms errors are compared to the standard (2,4) scheme for the proposed methods. The optimized methods are second-order accurate in space and have higher accuracy than the standard (2,4) scheme. It has been found that the dispersion error of the (2,4) scheme is like that of a second-order accurate method, though it behaves like a fourth-order accurate method in terms of anisotropy.
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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