Highly Efficient Boundary Element Analysis of Whispering Gallery Microcavities
Bibliographic record
Abstract
We demonstrate that the efficiency of the boundary element method, as applied to whispering gallery microcavity analyses, can be improved by orders of magnitude with the inclusion of the Fresnel technique. Using a scalar formulation, simulations of a microdisk with wavenumber-radius product as large as kR ≈ 8000 are achieved in contrast to a previous record of kR ≈ 100. In addition to its high accuracy for computing the modal field distributions and resonant wavelength, this technique yields a relative error of 10% when employing a direct root searching approach to calculate quality factors as high as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> (which are otherwise unattainable by a conventional boundary element method, due to computational limitations). Quadrupole-shaped and double disk cavities as large as 100 μm in diameter are also modeled by employing as few as 512 boundary elements, where simulations of such cavities using the conventional boundary element method have yet to be reported.
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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 | 0.001 | 0.001 |
| 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".