An efficient method using finite elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating
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Bibliographic record
Abstract
This work presents a novel finite element solution to the problem of scattering from an infinite periodic array of two‐dimensional cavities in metallic walls. The finite element 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 employing the quasi‐periodic Green's function is applied at the opening of the cavity as a boundary constraint to truncate the computational domain. Effect of the infinite array of cavities is incorporated into the system of the nodal equations by the quasi‐periodic Green's function. The method presented here is highly efficient in terms of computing resources, versatile and accurate in comparison to previously published methods. The near and far fields are generated for array of cavities with different dimensions, periodicity, and fillings. The numerical simulation results are in close agreement with methods published earlier.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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