Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms for\n Parabolic Problems
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We present a waveform relaxation version of the Dirichlet-Neumann and\nNeumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann\nmethod for steady problems, the method is based on a non-overlapping spatial\ndomain decomposition, and the iteration involves subdomain solves with\nDirichlet boundary conditions followed by subdomain solves with Neumann\nboundary conditions. For the Neumann-Neumann method, one step of the method\nconsists of solving the subdomain problems using Dirichlet interface\nconditions, followed by a correction step involving Neumann interface\nconditions. However, each subdomain problem is now in space and time, and the\ninterface conditions are also time-dependent. Using Laplace transforms, we show\nfor the heat equation that when we consider finite time intervals, the\nDirichlet-Neumann and Neumann-Neumann methods converge superlinearly for an\noptimal choice of the relaxation parameter, similar to the case of Schwarz\nwaveform relaxation algorithms. The convergence rate depends on the size of the\nsubdomains as well as the length of the time window. For any other choice of\nthe relaxation parameter, convergence is only linear. We illustrate our results\nwith numerical experiments.\n
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.
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) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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