Optimal Runge-Kutta Stability Polynomials for Multidimensional High-Order Methods
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Bibliographic record
Abstract
In this paper we generate optimized Runge-Kutta stability polynomials for multidimensional discontinuous Galerkin methods recovered using the flux reconstruction approach. Results from linear stability analysis demonstrate that these stability polynomials can yield significantly larger time-step sizes for triangular, quadrilateral, hexahedral, prismatic, and tetrahedral elements with speedup factors of up to 1.97 relative to classical Runge-Kutta methods. Furthermore, performing optimization for multidimensional elements yields modest performance benefits for the triangular, prismatic, and tetrahedral elements. Results from linear advection demonstrate these schemes obtain their designed order of accuracy. Results from Direct Numerical Simulation (DNS) of a Taylor-Green vortex demonstrate the performance benefit of these schemes for unsteady turbulent flows, with negligible impact on accuracy.
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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 | 0.002 | 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