An Algebraic Multigrid Method for the Finite Element Analysis of Large Scattering Problems
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Bibliographic record
Abstract
An efficient iterative solver is proposed for the linear matrix equation that arises in the analysis of large scattering problems by the frequency-domain finite-element method. A Krylov method is preconditioned by a technique that approximately solves equivalent problems in two auxiliary spaces: a space of scalar functions and a space of piecewise linear, “nodal,” vector functions. On each space the traditional algebraic multigrid method is employed. Further, the “shifted Laplace” idea is used to improve the performance of the solver as the frequency increases. Results are reported for a waveguide cavity filter and three free-space scatterers: a conducting sphere, a metallic frequency selective surface, and a metamaterial lens made of split-ring resonators containing dielectric and metal.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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