Application of the augmented block Householder Arnoldi method to the calculation of non-fundamental modes of the diffusion equation
Bibliographic record
Abstract
The determination of non-fundamental modes of the diffusion equation is required for computing CANDU reactor power distribution from analysis of in-core detector readings. They are also important for understanding subcritical mode instabilities occurring in boiling water reactors. The legacy method for computing these modes is the Hotelling deflation technique based on bi-harmonic decontamination. However, the Hotelling technique becomes unstable as the number of modes increase or as their eigenvalues become closer. Effective and fast alternatives are provided with Implicit Arnoldi Restarted Methods (IRAM). Among them, we investigated the Krylov–Schur method available in the SLEPc library, and we are proposing a custom implementation of the augmented block Householder Arnoldi (ABHA) method, similar to the Open Source implementation of Prof. James Baglama. In our work, the ABHA method is applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas-Schneider methods or with the mesh-centered finite difference method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".