On Dissipation and Dispersion Errors Optimization, A-Stability and SSP Properties
Bibliographic record
Abstract
In a recent paper (Du and Ekaterinaris, 2016) optimization of dissipation and dispersion errors was investigated.A Diagonally Implicit Runge-Kutta (DIRK) scheme was developed by using the relative stability concept, i.e. the ratio of absolute numerical stability function to analytical one.They indicated that their new scheme has many similarities to one of the optimized Strong Stability Preserving (SSP) schemes.They concluded that, for steady state simulations, time integration schemes should have high dissipation and low dispersion.In this note, dissipation and dispersion errors for DIRK schemes are studied further.It is shown that relative stability is not an appropriate criterion for numerical stability analyses.Moreover, within absolute stability analysis, it is shown that there are two important concerns, accuracy and stability limits.It is proved that both A-stability and SSP properties aim at minimizing the dissipation and dispersion errors.While A-stability property attempts to increase the stability limit for large time step sizes and by bounding the error propagations via minimizing the numerical dispersion relation, SSP optimized method aims at increasing the accuracy limits by minimizing the difference between analytical and numerical dispersion relations.Hence, it can be concluded that A-stability property is necessary for calculations under large time-step sizes and, more specifically, for calculation of high diffusion terms.Furthermore, it is shown that the oscillatory behavior, reported by Du and Ekaterinaris (2016), is due to Newton method and the tolerances they set and it is not related to the employed temporal schemes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".