A Newton-Krylov Approach for Aerodynamic Shape Optimization of Wings
Bibliographic record
Abstract
A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and a quasi-Newton method to find the optimum. The Krylov subspace method flexible generalized minimal residual is used with approximate-Schur preconditioning to solve both the flow equation and the adjoint equation in a parallel computing environment. The wing geometry is parameterized by a B-spline control net, and a fast algebraic algorithm is used for grid movement. The discrete-adjoint gradient can be obtained in approximately one-fourth the time required for a converged flow solution. The accuracy of the gradient is compared against finite differencing and is found to be comparably accurate. A single-point test case is presented for a cruise configuration optimization at transonic speed. This example as well as an inverse design demonstrate that the optimizer is able to decrease the objective function and gradient by several orders of magnitude efficiently for problems with over 170 design variables. I.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".