A hybrid finite element method - surface integral equation using quasi-periodic green's function in solving the problem of scattering from infinite periodic conducting grating
Bibliographic record
Abstract
In this paper, we develop a new FEM-based method to solve the problem of scattering from an infinite periodic array of identical cavities engraved in an infinite perfect electric conductor screen. The FEM formulation is applied inside only one cavity to derive a linear system of equations associated with the nodal field values within the cavity. The surface integral equation using the free-space Green's function is applied at the openings of all cavities as a global boundary condition. Taking advantage of field's periodicity at the apertures of the cavities, the free space Green's function is replaced by the quasi-periodic Green's function, thus limiting the surface integral equation to the aperture of only one cavity. The advantage of this method is that no periodic boundary condition which would require a constrained mesh scheme is used in this formulation. Also we emphasize that in the method presented here, the surface integral equation using the quasi-periodic Green's function is used to derive a linear system of equation as a constraint which connects the field values on the boundary to the field values on the apertures of the single cavity in the array by considering the coupling between all cavities.
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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 | 0.001 | 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) | 0.001 | 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 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".