Formulation and Analysis of Implicit IE-GSTC Metasurface Forward Solver
Bibliographic record
Abstract
This paper first extends an integral equation (IE) based zero-thickness metasurface forward solver known as the implicit (IMP) IE-GSTC method to account for composite metasurface problems consisting of multiple metasurfaces and additional dielectric scattering objects. This extension is followed by the development of a unified mathematical framework that is used to analyze and compare the formulation of different IE-based zero-thickness metasurface forward solvers. It is shown that all of these IE-based zero-thickness metasurface forward solvers are analytically equivalent. Despite this analytical equivalence, we demonstrate that there exist key numerical differences between the formulations, which can affect the computational performance of each method. We conclude the paper by first comparing the performance of the extended IMP IE-GSTC method, applied to composite metasurface problems utilizing zero-thickness metasurface models, to that of a commercial full-wave forward solver that utilizes finite-thickness metasurface models. Finally, we conduct a comparison between the numerical performance of the IMP IE-GSTC and those of the other IE-based zero-thickness methods.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 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".