Mesh Movement for a Discrete-Adjoint Newton-Krylov Algorithm for Aerodynamic Optimization
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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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".