Matrix-Explicit GMRES for a Higher-Order Accurate Inviscid Compressible Flow Solver
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Bibliographic record
Abstract
Implicit methods for nite-volume schemes on unstructured grids typically rely on a matrix-free implementation of GMRES and an explicit rst-order Jacobian for preconditioning. We show that it is possible to form the higher-order Jacobian explicitly at a reasonable computational cost. This is demonstrated for cases using both limited and unlimited reconstruction. The bene ts resulting from improvements in preconditioning and the elimination of residual evaluations in the inner iterations of the matrix-free GMRES method are substantial. Computational results are presented for 2nd, 3rd, and 4th order accurate schemes. Overall computational cost for the matrix-explicit method is lower than the matrix-free method for all cases. The fourth-order matrix-explicit scheme is a factor of 2.5 to 3 faster than the matrix-free scheme while using only about 50% more memory.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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