Algebraic Multigrid Combined With Domain Decomposition for the Finite Element Analysis of Large Scattering Problems
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Bibliographic record
Abstract
In the finite element analysis of electromagnetic scattering, a recent algebraic multigrid method (Aghabarati and Webb, “An Algebraic Multigrid Method for the Finite Element Analysis of Large Scattering Problems,” IEEE Trans. Antennas Propag., vol. 61, no, 2, pp. 809-817, Feb. 2013) has been shown to be an efficient way to solve the large, sparse matrix equation. However, the effectiveness of the method decreases as the electrical size of the problem increases. This limitation is overcome by combining it with a domain decomposition method (DDM). Exact solution on each domain is not needed: a single W-cycle of the multigrid method is sufficient. Results are presented for scattering of plane waves by conducting and dielectric objects, with dimensions ranging from 3 wavelengths to 20 wavelengths.
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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) | 0.000 | 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) | 0.000 | 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