Compensating for time stepping errors locally in the pseudo‐analytical method using normalized pseudo‐Laplacian
Bibliographic record
Abstract
The pseudo-analytical method relies on pseudo-Laplacians to compensate for time stepping errors caused by the second-order time stepping scheme. Pseudo-Laplacian slowly varies with the compensation velocity which makes it well suited for models with mild velocity variations. For models with high velocity variations, the pseudo-analytical method becomes difficult because high compensation velocities cause over-compensations to wavefields in low velocity areas which can bring significant artifacts into the simulation results. To tackle this problem, I propose to use spatially varying normalized pseudo-Laplacians, which are determined by actual velocity variations in space, to locally compensate for time stepping errors. This new implementation of the pseudo-analytical method involves two steps. The first step applies local compensations using adaptive normalized pseudo-Laplacians, computed either in wavenumber domain or in space domain. The second step carries out the second-order time marching computations, which can be realized by any numerical schemes and not limited to the wavenumber domain method. I use numerical experiments to demonstrate that the proposed method can produce highly accurate results with relaxed stability conditions compared to the conventional pseu-dospectral method.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".