Optimized Schwarz domain decomposition approaches for the generation of equidistributing grids
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Bibliographic record
Abstract
The main purpose of this thesis is to develop and analyze iterations arising from domain \ndecomposition methods for equidistributing meshes. Adaptive methods are powerful techniques \nto obtain the efficient numerical solution of physical boundary value problems \n(BVPs) which arise from science and engineering. If a solution of a BVP has sharp changes, \nequidistributed mesh can give a reasonable solution for the BVP with a fixed number of \nmesh points. Our concern is to solve the involved nonlinear mesh BVP using optimized \ndomain decomposition approaches and efficiently provide a nonuniform coordinate for the \noriginal boundary value problem. We derive an implicit solution on each subdomain from \nthe optimized Schwarz method for the mesh BVP, and then introduce an interface iteration \nfrom the Robin transmission condition, which is a nonlinear iteration. Using the theory of \nM-functions we provide an alternate analysis of the optimized Schwarz method on two subdomains \nand extend this result to an arbitrary number of subdomains. M-function theory \nguarantees that these iterations will converge monotonically under some restriction on p, \nwhere p is the Robin parameter. The iteration can be computed by nonlinear (block) Gauss \nJacobi or Gauss Seidel methods. We conclude our study with numerical experiments.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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