Solving arbitrary resonant structures with an efficient eigen-based MRTD formulation
Bibliographic record
Abstract
Numerical computation of a high-Q resonant structure may pose as a challenge for its requirements computation time and memory. Circumvent the problem, we developed an eigen-based formulation, called the "Spatial Multi-Resolution Time-Domain (SPATIAL-MRTD) method, based on the recently developed MRTD method. In it, wavelets are used to expand the electromagnetic fields in spatial domain while the time differentials are kept with the Maxwell's equations. The final formulation is a sparse eigenvalue problem. By applying the sparse matrix techniques, resonant frequencies and modes are obtained effectively and efficiently. Like MRTD, low number of spatial grid points (as low as two points per wavelength) is required. Unlike MRTD, direct recursive time-marching calculations are not needed. As a result, the method is numerical-instability free. In addition, no post-simulation data-processing, such as discrete Fourier Transform, is required.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".