MODIFIED FIXED-GRID FINITE ELEMENT METHOD IN SHAPE OPTIMIZATION PROBLEMS BASED ON THE GRADIENTLESS METHOD
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Bibliographic record
Abstract
This paper presents a methodology for solving shape optimization problemswhere the unknown is the shape of the problem domain. The proposed algorithm is based on the minimization of the stress along design boundary calculated by the Modified Fixed Grid Finite Element Method (MFGFEM). Using MFGFEM eliminates mesh adaptation and re-meshing processes as needed in the standard finite element method and reduces the analysis cost significantly. In this study, a new approach for computing stiffness matrix of boundary intersecting elements is also presented and optimal shape of the problem domain is obtained via a simple optimization algorithm.The performance of the proposed approach is investigated for the shape optimization problems. It is concluded that the results of the present method are in a good agreement with other analytical and finite element solutions.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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