Dynamic Mode Decomposition For Improved Numerical Stability of Finite Volume Simulations
Bibliographic record
Abstract
We propose a novel approach to mesh optimization for improved stability of finite-volume simulations using dynamic mode decomposition on a subset of the solution vectors. A minimal number of the most recent solution vectors in the simulation are selected for dynamic mode decomposition. The eigenvalues of the Koopman matrix depict the magnitude growth rate and oscillation frequency of the largest solution modes. The computational cost of this method depends on the number of solution vectors in use, which is considerably less expensive compared to the eigenanalysis of the full Jacobian matrix. The dynamic eigenvectors are utilized to identify which control volumes and vertices have the greatest impact on each dynamic solution mode. The gradients of the Jacobian matrix diagonal are calculated with respect to the movement of the selected vertices. The positions of these points are adjusted to increase the diagonal dominance of the Jacobian matrix on the corresponding rows. The results verify the effectiveness and feasibility of the novel approach in numerical stability improvement through unstructured mesh optimization. This state-of-the-art method addresses the challenges faced by the latest studies in this field with full automation of the mesh optimization process and substantial computational savings.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".