Legendre Spectral Galerkin Method for Electromagnetic Scattering from Large Cavities
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Bibliographic record
Abstract
The paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane, which is governed by a Helmholtz type equation with nonlocal hypersingular transparent boundary condition on the aperture. We first present some stability estimates with the explicit dependency of wavenumber for the Helmholtz type cavity problem. Then a Legendre spectral Galerkin method is proposed, in which the Legendre--Gauss interpolatory approximation is applicable to the hypersingular integral and a Legendre--Galerkin scheme is used for the approximation to the Helmholtz equation. The existence and the uniqueness of the approximation solution are established for large wavenumbers; the stability and the spectral convergence of the numerical method are then proved. Illustrative numerical results presented confirm our theoretical estimates and show that the proposed spectral method, compared with low-order finite difference methods, is especially effective for problems with large wavenumbers.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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