Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods
Bibliographic record
Abstract
Abstract The numerical dispersion of a proposed new FDTD scheme is often evaluated and compared with that of well‐established FDTD methods. Because there may be a theoretical deficiency in the dispersion analysis, numerical experimentation is often used to validate the dispersion relation. This paper describes the “matching method” for validation using a cylindrical wave in the two‐dimensional (2D) case. The matching method is demonstrated by evaluating the numerical dispersion of Yee's FDTD and ADI‐FDTD. The result is compared with the analytical numerical dispersion relation, and excellent agreement is obtained. The difference between the theoretical value for the numerical dispersion and that from numerical experiments using the matching method is 10−5 for Yee's FDTD and 10−4–10−5 for ADI‐FDTD. The numerical velocity obtained from the matching method satisfies the theoretical dispersion relation with residual errors to the order of 10−6. Such accuracy is sufficient to conclude that a numerical dispersion relation is correct. Although the matching method uses a cylindrical wave to test the numerical dispersion relation, the cylindrical wave is not a solution of the difference equations, thus it cannot be used to derive a theoretical dispersion relation. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 138–142, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20400
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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 | 0.006 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".