Domain decomposition of stochastic PDEs: Theoretical formulations
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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.
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- Candidate signal: MethodsConsensus signal: Methods
- Teacher disagreement score
- 0.435
- Threshold uncertainty score
- 0.802
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
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|---|---|---|
| Metaresearch | 0.003 | 0.007 |
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| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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- Teacher spread
- 0.379 · how far apart the two teachers sit on this one work
- Validation status
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
Abstract
Abstract We present a novel theoretical framework for the domain decomposition of uncertain systems defined by stochastic partial differential equations. The methodology involves a domain decomposition method in the geometric space and a functional decomposition in the probabilistic space. The probabilistic decomposition is based on a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes. The spatial decomposition is achieved through a Schur‐complement‐based domain decomposition. The methodology aims to exploit the full potential of high‐performance computing platforms by reducing discretization errors with high‐resolution numerical model in conjunction to giving due regards to uncertainty in the system. The mathematical formulation is numerically validated with an example of waves in random media. Copyright © 2008 John Wiley & Sons, Ltd.
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The record
- Venue
- International Journal for Numerical Methods in Engineering
- Topic
- Probabilistic and Robust Engineering Design
- Field
- Decision Sciences
- Canadian institutions
- University of OttawaCarleton University
- Funders
- Sandia National LaboratoriesNatural Sciences and Engineering Research Council of CanadaCanada Research ChairsAir Force Office of Scientific ResearchOntario Innovation Trust
- Keywords
- Domain decomposition methodsDiscretizationDecompositionProbabilistic logicDomain (mathematical analysis)Decomposition method (queueing theory)Applied mathematicsSchur complementComplement (music)MathematicsMortar methodsMathematical optimizationPartial differential equationComputer scienceAlgorithmFinite element methodMathematical analysisDiscrete mathematics
- Has abstract in OpenAlex
- yes