Optimized Schwarz domain decomposition approaches for the generation of equidistributing grids
Bibliographic record
Abstract
The main purpose of this thesis is to develop and analyze iterations arising from domain decomposition methods for equidistributing meshes. Adaptive methods are powerful techniques to obtain the efficient numerical solution of physical boundary value problems (BVPs) which arise from science and engineering. If a solution of a BVP has sharp changes, equidistributed mesh can give a reasonable solution for the BVP with a fixed number of mesh points. Our concern is to solve the involved nonlinear mesh BVP using optimized domain decomposition approaches and efficiently provide a nonuniform coordinate for the original boundary value problem. We derive an implicit solution on each subdomain from the optimized Schwarz method for the mesh BVP, and then introduce an interface iteration from the Robin transmission condition, which is a nonlinear iteration. Using the theory of M-functions we provide an alternate analysis of the optimized Schwarz method on two subdomains and extend this result to an arbitrary number of subdomains. M-function theory guarantees that these iterations will converge monotonically under some restriction on p, where p is the Robin parameter. The iteration can be computed by nonlinear (block) Gauss Jacobi or Gauss Seidel methods. We conclude our study with numerical experiments.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".