Numerical dispersion and numerical loss in explicit finite-difference time-domain methods in lossy media
Bibliographic record
Abstract
The numerical dispersion relations of finite-difference time-domain (FDTD) methods have been analyzed extensively in lossless media. This paper investigates numerical dispersion and loss for Yee's FDTD in lossy media. It is shown that: the numerical velocity can be smaller or larger than the physical velocity; there is no "magic time step size" in lossy media; and the numerical loss is smallest at the Courant limit. It is shown that the numerical loss is always larger than its physical value, and so Yee's FDTD overestimates the absorption of electromagnetic energy in lossy media. The numerical velocity anisotropy can be positive or negative, but the numerical loss anisotropy is always positive. The anisotropies in the three-dimensional (3-D) case are usually larger than those in the 2-D case. Numerical experiments in 1-D are shown to agree with the theoretical prediction.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.011 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".