Mesh Movement for a Discrete-Adjoint Newton-Krylov Algorithm for Aerodynamic Optimization
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Bibliographic record
Abstract
A grid movement algorithm based on the linear elasticity method with multiple increments is presented. The method is relatively computationally expensive but is exceptionally robust, producing high-quality elements even for large shape changes. It is integrated with an aerodynamic shape optimization algorithm that uses an augmented adjoint approach for gradient calculation. The discrete-adjoint equations are augmented to explicitly include the sensitivities of the mesh movement, resulting in an increase in efficiency and numerical accuracy. This gradient computation method requires less computational time than a function evaluation and leads to significant computational savings as dimensionality is increased. The results of the application of these techniques to several large deformation and optimization cases are presented. Nomenclature A = coordinates of the airfoil surface E = modulus of elasticity f = external forces G = coordinates of the interior grid nodes J, F = objective functions i = increment number K = stiffness matrix L = Lagrangian l = length of a side of a triangle n = number of increments P = potential energy Q = flow variables R = radius of a circumscribed circle R = flow residual r = residual of the grid movement equations s = semiperimeter of a triangle u = element displacements V = element volume X = design variables = boundary , = adjoint vector = radius of an inscribed circle = stress tensor = element shape quality = spatial domain Subscripts e = belonging to an element t = belonging to the entire system jQ = Q is held constant in the differentiation = subtriangular element inside a quadrilateral Superscripts ^ = known variable on the boundary T = transpose
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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