Generalization of the Finite-Difference-Based Time-Domain Methods Using the Method of Moments
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Bibliographic record
Abstract
Many finite-difference-based time-domain methods have been developed in the past three decades. Typical among them are the finite-difference time-domain method of Yee's scheme, the transmission-line-matrix method, the multiresolution time-domain method, the pseudospectral time-domain method, and the unconditionally stable finite-difference time-domain methods. All these methods have become powerful tools in solving electromagnetic structure problems, yet their formulations appear to be unrelated. The concept of the method of moments (MoM) is applied in this paper to generalize all these different finite-difference-based methods. It is shown theoretically that differences among various finite-difference-based methods lie in different choices of basis functions used in solution expansions and weighting functions in error testing, in both time and space. The significance of this paper is twofold: 1) all the finite-difference time-domain-based methods can now be unified under the framework of MoM and 2) any other new finite-difference-based time-domain methods, including hybrid techniques, may now be developed with MoM procedure
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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 | 0.000 | 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