A PDE sensitivity equation method for optimal aerodynamic design
type: Item
instance of: scholarly article
title: A PDE sensitivity equation method for optimal aerodynamic design
zbMATH Open document ID: 0903.76064
author: Jeff T. Borggaard
author: John A. Burns
published in: Journal of Computational Physics
publication date: 1997-12-15T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19970006726
review text: The authors investigate a problem of shape optimization for aerodynamic applications. It is suggested to find design sensitivities in form of a sensitivity equation which is obtained by implicitly differentiating the infinite-dimensional state equation with respect to the design parameters. This approach leads to computational advantages compared to other methods, and further the approach provides that the sensitivity equation is always linear in the design sensitivity. The sensitivity equation is presented and analyzed. Space optimization is demonstrated for the simulation of Euler flows over a forebody and of certain duct flows. In addition to the discussion of these two examples, the sensitivity equation method is compared to other methods. Also included are discussions of convergence issues and a convergence theorem for the sensitivity equation method. The paper is interesting to read. It gives a lot of the essential details of the method proposed.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76G25
zbMATH DE Number: 1084037
zbMATH Keywords: Euler flows over forebody
zbMATH Keywords: shape optimization
zbMATH Keywords: infinite-dimensional state equation
zbMATH Keywords: duct flows
zbMATH Keywords: convergence theorem
MaRDI profile type: Publication
OpenAlex ID: W1996568929
cites work: An implicit finite-difference algorithm for hyperbolic systems in conservation-law form
cites work: Q4273771
cites work: Q4882072
cites work: On the Global Convergence of Trust Region Algorithms Using Inexact Gradient Information
cites work: An Adaptive Nonlinear Least-Squares Algorithm
cites work: Q3702408
cites work: Q4041056
cites work: A comparison of optimization-based approaches for a model computational aerodynamics design problem
cites work: Computing Optimal Locally Constrained Steps
cites work: Numerical simulation and optimal shape for viscous flow by a fictitious domain method
cites work: The Local Convergence of Broyden-Like Methods on Lipschitzian Problems in Hilbert Spaces
cites work: Design sensitivity analysis of structural systems
cites work: Aerodynamic design via control theory
cites work: A discrete semianalytical procedure for aerodynamic sensitivity analysis including grid sensitivity
cites work: On optimum profiles in Stokes flow
cites work: On optimum design in fluid mechanics
cites work: Q3732914
DOI: 10.1006/JCPH.1997.5743
description: scientific article; zbMATH DE number 1084037