## An Introduction to the Adjoint Approach to Design (2000)

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Citations: | 53 - 10 self |

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@MISC{Giles00anintroduction,

author = {Michael B. Giles and Niles A. Pierce},

title = { An Introduction to the Adjoint Approach to Design},

year = {2000}

}

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### Citations

1346 |
Practical Optimization
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Citation Context ... cycle is relatively low. In the second approach, approximations to the Hessian matrix of second derivatives d 2 J d i d j ; are used to speed convergence via a quasi-Newton procedure such as BFGS (Gi=-=ll et al., 198-=-1). This method therefore requires more accuratesow and adjoint solutions, which must generally be converged fully during each design iteration. As a result, the cost of each design cycle is signicant... |

302 | Optimal Control of Systems Governed by Partial Differential Equations - Lions - 1971 |

204 | Aerodynamic Design via Control Theory - Jameson - 1988 |

149 | Generating derivative codes from Fortran programs
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- 1991
(Show Context)
Citation Context ... for characteristic smoothingsuxes for the Euler equations. An alternative is to use AD (Automatic Dierentiation) software such as Odyssee (Gilbert et al., 1991; Faure, 1996) or ADIFOR and ADJIFOR (Bi=-=schof et al., 1992-=-; Carle et al., 1998) to generate the Fortran code to compute the product L T e v. In forward mode, AD software takes the original code which computed R e (U) and then uses the basic rules of linearis... |

107 | Optimum Aerodynamic Design Using the Navier-Stokes Equations, Theoret
- Jameson, Martinelli, et al.
- 1998
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Citation Context ...ome objective function subject to a set of constraints. In a sequence of papers by himself (1988; 1995a; 1995b) and with Reuther and other co-authors (Reuther and Jameson, 1994; Reuther et al., 1996; =-=Jameson et al., 1998-=-) Jameson developed the adjoint approach for potentialsow, the Euler equations and the Navier-Stokes equations. The complexity of the applications within these papers also progressed from 2D airfoil o... |

101 | Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation
- Anderson, Venkatakrishnan
- 1999
(Show Context)
Citation Context ...roups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; Ta'asan et al., 1992; Baysal and Eleshaky, 1992; Human et al., 1993; Lewis and Agarwal, 1995; A=-=nderson and Venkatakrishnan, 1999-=-; Dadone and Grossman, 1999). An overview of recent developments in adjoint design methods is provided elsewhere (Newman et al., 1999). Of particcs2000 Kluwer Academic Publishers. Printed in the Nethe... |

82 |
User’s guide for NPSOL (version 4.0): A Fortran package for nonlinear programming
- Gill, Murray, et al.
- 1986
(Show Context)
Citation Context ...onstraints are imposed on maximum thickness, spar thickness, leading edge bluntness and trailing edge angle. The results were obtained aftersve design iterations using the optimization package NPSOL (=-=Gill et al., 198-=-6) during which the interior grid points were perturbed using WARP-MB (Reuther et al., 1999a). The initial conguration was designed for cruise at M = 0:8 and CL = 0:3 and the three new design points a... |

76 |
Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers: Part II
- Reuther, Jameson, et al.
- 1998
(Show Context)
Citation Context ...r-Stokes equations. The complexity of the applications within these papers also progressed from 2D airfoil optimisation, to 3D wing design andsnally to complete aircraft congurations (Jameson, 1999; R=-=euther et al., 1999-=-a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; Ta'asan et al., 1992; Baysal and Eleshak... |

55 | Adjoint recovery of superconvergent functionals from PDE approximations
- Pierce, Giles
(Show Context)
Citation Context ...n to constrained optimisation and optimal control theory. On the other hand, we prefer the duality viewpoint because it seems more natural for other uses of adjoint variables, such as error analysis (=-=Pierce and Giles, 1998-=-; Giles and Pierce, 1999; Venditti and Darmofal, 1999; Pierce and Giles, 2000), which do not involve constrained optimisation. 2.6. Nonlinear optimisation Returning to the design problem, the aim is t... |

54 |
W ing design by numerical optimization
- Hicks, Henne
- 1978
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Citation Context ...is work employs a continuous adjoint formulation on a structured multiblock mesh using parallel multigridsow and adjoint solvers. The wing surface is parameterised with 18 Hicks-Henne bump functions (=-=Hicks and Henne, 1978-=-) at each ofsve span stations and a total of 30 constraints are imposed on maximum thickness, spar thickness, leading edge bluntness and trailing edge angle. The results were obtained aftersve design ... |

48 |
Optimum aerodynamic design using control theory
- Jameson
- 1995
(Show Context)
Citation Context ...antage of this method is that partially-convergedsow and adjoint solutions may be used to evaluate the gradients as long as these gradients are properly smoothed (preconditioned) prior to updating (J=-=ameson, 19-=-95b). As a result, the cost per design cycle is relatively low. In the second approach, approximations to the Hessian matrix of second derivatives d 2 J d i d j ; are used to speed convergence via a q... |

43 | Optimum aerodynamic design using CFD and control theory. AIAA paper 951729
- Jameson
- 1995
(Show Context)
Citation Context ...antage of this method is that partially-convergedsow and adjoint solutions may be used to evaluate the gradients as long as these gradients are properly smoothed (preconditioned) prior to updating (J=-=ameson, 19-=-95b). As a result, the cost per design cycle is relatively low. In the second approach, approximations to the Hessian matrix of second derivatives d 2 J d i d j ; are used to speed convergence via a q... |

42 |
Numerical Grid Generation: Foundations and Applications
- Thompson, Warsi, et al.
- 1985
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Citation Context ...) N(U;X()) = 0; where X is the vector of grid point coordinates which depends on . Using techniques such as the `method of springs' (Rausch et al., 1993) or variants on transnite interpolation (Thomp=-=son et al., 198-=-5; Reuther et al., 1996), the grid deforms smoothly as changes in the design variables modify the surface geometry. Hence, @X=@ is usually non-zero at both interior and surface grid points. For a sing... |

35 | On Optimum Design in Fluid Mechanics - Pironneau |

34 |
Eleshaky, Aerodynamic design optimization using sensitivity anaysis and computational fluid dynamics
- Baysal, E
- 1991
(Show Context)
Citation Context ...uther et al., 1999a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; Ta'asan et al., 1992; =-=Baysal and Eleshaky, 199-=-2; Human et al., 1993; Lewis and Agarwal, 1995; Anderson and Venkatakrishnan, 1999; Dadone and Grossman, 1999). An overview of recent developments in adjoint design methods is provided elsewhere (Newm... |

33 | Practical 3D aerodynamic design and optimization using unstructured meshes - Elliot, Peraire - 1996 |

32 | Aerodynamic shape optimization of complex aircraft configurations via an adjoint method - Reuther, Jameson, et al. - 1996 |

31 | Improved lift and drag estimates using adjoint euler equations
- Giles, Pierce
- 1999
(Show Context)
Citation Context ...ation and optimal control theory. On the other hand, we prefer the duality viewpoint because it seems more natural for other uses of adjoint variables, such as error analysis (Pierce and Giles, 1998; =-=Giles and Pierce, 1999-=-; Venditti and Darmofal, 1999; Pierce and Giles, 2000), which do not involve constrained optimisation. 2.6. Nonlinear optimisation Returning to the design problem, the aim is tosnd the set of design v... |

30 | Adjoint equations in CFD: duality, boundary conditions and solution behaviour
- Giles, Pierce
- 1997
(Show Context)
Citation Context ...ndary integral terms in the primal objective function lead to inhomogeneous b.c.'s for the adjoint, while inhomogeneous b.c.'s for the primal problem lead to boundary terms in the adjoint functional (=-=Giles and Pierce, 1-=-997). The general form of the adjoint identity is (V; LU) + (C V; BU) @ = (L V; U) + (B V; CU) @ for all functions U; V , with the notation (:; :) @ denoting an inner product over the boundary. B a... |

27 | 17 of sensitivity analysis and shape optimization for complex aerodynamic configurations - Barnwell, Newman, et al. - 1999 |

27 | Using complex variables to estimate derivatives of real functions - Squire, Trapp - 1998 |

25 | Aerodynamic Design Using Unstructured Meshes,” AIAA Paper 96-1941
- Elliot, Peraire
- 1996
(Show Context)
Citation Context ...ges over the other in terms of design performance. Ultimately, thesnal choice may always remain, to some extent, a matter of personal taste. 5. Application Results from a paper by Elliot and Peraire (=-=Elliott and Peraire, 1996-=-) show the use of a discrete adjoint implementation for design optimisation on unstructured grids. The main application considered is the wing optimisation of a business jet for which the surface grid... |

25 |
Aerodynamic design and optimization in one shot
- Ta’asan, Kuruvila, et al.
(Show Context)
Citation Context ...ons (Jameson, 1999; Reuther et al., 1999a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; =-=Ta'asan et al., 199-=-2; Baysal and Eleshaky, 1992; Human et al., 1993; Lewis and Agarwal, 1995; Anderson and Venkatakrishnan, 1999; Dadone and Grossman, 1999). An overview of recent developments in adjoint design methods ... |

23 |
Re-engineering the design process through computation. AIAA paper 97-0641, 35th Aerospace Sciences Meeting and Exhibit
- Jameson
- 1997
(Show Context)
Citation Context ...s and the Navier-Stokes equations. The complexity of the applications within these papers also progressed from 2D airfoil optimisation, to 3D wing design andsnally to complete aircraft congurations (J=-=ameson, 1999-=-; Reuther et al., 1999a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; Ta'asan et al., 19... |

22 |
Airfoil design on unstructured grids for turbulent flows
- Anderson, Bonhaus
- 1999
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Citation Context ...ademic Publishers. Printed in the Netherlands. paper.tex; 22/02/2000; 11:18; p.1 2 M.B. Giles & N.A. Pierce ular interest is the work of Elliott (1997; 1998) and Anderson (Nielsen and Anderson, 1998; =-=Anderson and Bonhaus, 199-=-9) on unstructured grids using the `discrete' adjoint approach, and the work of Mohammadi (1997a; 1997b) in using automatic dierentiation software to create the adjoint code from an original CFD code;... |

18 | Sensitivity analysis for the Navier-Stokes equations on unstructured meshes using complex variables. AIAA paper 99-3294 - Anderson, Newman, et al. - 1999 |

18 | On the properties of solutions of the adjoint Euler equations
- Giles, Pierce
- 1998
(Show Context)
Citation Context ...on process. When considering shocked Eulersows, then in the analytic formulation, the shocks need to be treated as discontinuities across which the Rankine-Hugoniot shock jump relations are enforced (=-=Giles and Pierce, 1998-=-). This treatment leads to the result that the adjoint variables are continuous across the shock and that an additional adjoint boundary condition must be imposed along the length of the shock. Imposi... |

16 | Preliminary results from the application of automated adjoint code generation to CFL3D. AIAA paper
- Carle, Fagan, et al.
- 1998
(Show Context)
Citation Context ...oothingsuxes for the Euler equations. An alternative is to use AD (Automatic Dierentiation) software such as Odyssee (Gilbert et al., 1991; Faure, 1996) or ADIFOR and ADJIFOR (Bischof et al., 1992; Ca=-=rle et al., 1998-=-) to generate the Fortran code to compute the product L T e v. In forward mode, AD software takes the original code which computed R e (U) and then uses the basic rules of linearisation to construct t... |

15 | On automatic dierentiation - Griewank - 1989 |

15 | différentiation automatique de fonctions représentées par des programmes - Gilbert, Vey, et al. - 1991 |

13 | A.: “On Automatic Differentiation.” Mathematical Programming: Recent Developments and Applications - Griewank - 1989 |

11 |
Three-dimensional timemarching aeroelastic analyses using an unstructured-grid Euler method
- Rausch, Batina, et al.
- 1993
(Show Context)
Citation Context ... are all satised. These may be expressed collectively as N(U;) N(U;X()) = 0; where X is the vector of grid point coordinates which depends on . Using techniques such as the `method of springs' (Rausc=-=h et al., 19-=-93) or variants on transnite interpolation (Thompson et al., 1985; Reuther et al., 1996), the grid deforms smoothly as changes in the design variables modify the surface geometry. Hence, @X=@ is usual... |

9 | Aerodynamic optimization based on the Euler and Navier-Stokes equations using unstructured grids - Elliott - 1998 |

9 | Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations
- Giles
- 1996
(Show Context)
Citation Context ...aches give numerical results which converge to the analytic solution. For the discrete approach, this follows because the integrated pressure can be proved to be predicted with second order accuracy (=-=Giles, 1996-=-). The linearised discretisation should therefore yield perturbations to the integral of pressure that are at leastsrst-order accurate. The discrete adjoint formulation, which is constructed using thi... |

9 |
Sensitivity analysis, approximate analysis and design optimization for internal and external viscous AIAA Paper 913083
- Korivi, Taylor, et al.
- 1991
(Show Context)
Citation Context ...e aircraft congurations (Jameson, 1999; Reuther et al., 1999a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; K=-=orivi et al., 199-=-1; Ta'asan et al., 1992; Baysal and Eleshaky, 1992; Human et al., 1993; Lewis and Agarwal, 1995; Anderson and Venkatakrishnan, 1999; Dadone and Grossman, 1999). An overview of recent developments in a... |

8 | Optimal Shape Design, Reverse Mode of Automatic Differentiation - Mohammadi - 1997 |

8 | Control based airfoil design using the Euler equations. AIAA paper 94-4272-CP - Reuther, Jameson - 1994 |

8 | A Multilevel Error Estimation and Grid Adaptive Strategy for Improving the Accuracy of Integral Outputs,” AIAA Paper 1999-3292 - Venditti, Darmofal - 2008 |

7 |
Adjoint operator approach to shape design for internal incompressible flow
- Cabuk, Shung, et al.
- 1991
(Show Context)
Citation Context ...andsnally to complete aircraft congurations (Jameson, 1999; Reuther et al., 1999a; Reuther et al., 1999b). A number of other research groups have developed adjoint CFD codes for design optimisation (C=-=abuk et al., 199-=-1; Korivi et al., 1991; Ta'asan et al., 1992; Baysal and Eleshaky, 1992; Human et al., 1993; Lewis and Agarwal, 1995; Anderson and Venkatakrishnan, 1999; Dadone and Grossman, 1999). An overview of rec... |

7 | Splitting of algebraic expressions for automatic differentiation - Faure - 1996 |

7 | Practical Applications to Fluid Flows of Automatic Differentiation for Design Problems.VKI lecture series - Mohammadi - 1997 |

4 |
Splitting of algebraic expressions for automatic dierentiation
- Faure
- 1996
(Show Context)
Citation Context ...s in the Navier-Stokes equations and for characteristic smoothingsuxes for the Euler equations. An alternative is to use AD (Automatic Dierentiation) software such as Odyssee (Gilbert et al., 1991; Fa=-=ure, 1996-=-) or ADIFOR and ADJIFOR (Bischof et al., 1992; Carle et al., 1998) to generate the Fortran code to compute the product L T e v. In forward mode, AD software takes the original code which computed R e ... |

3 | La di erentiation automatique de fonctions representees par des programmes. Rapport de Recherche n o 1557 - Gilbert, Masse - 1991 |

3 |
Airfoil design via control theory using fullpotential and Euler equations
- Lewis, Agarwal, et al.
- 1995
(Show Context)
Citation Context ...umber of other research groups have developed adjoint CFD codes for design optimisation (Cabuk et al., 1991; Korivi et al., 1991; Ta'asan et al., 1992; Baysal and Eleshaky, 1992; Human et al., 1993; L=-=ewis and Agarwal, 1995-=-; Anderson and Venkatakrishnan, 1999; Dadone and Grossman, 1999). An overview of recent developments in adjoint design methods is provided elsewhere (Newman et al., 1999). Of particcs2000 Kluwer Acade... |

2 | On optimum design in mechanics - Pironneau - 1974 |

2 | Sensitivity Analysis for Navier– Stokes Equations on Unstructured Grids Using - Anderson, Nielsen |

2 | Practical design and optimization in computational fluid dynamics. AIAA Paper - Huffman, Melvin, et al. - 1993 |

1 | Practical applications to of automatic dierentiation for design problems - Mohammadi - 1997 |

1 | Aerodynamic shape optimization of complex aircraft con via an adjoint formulation - 94-4272-CP - 1994 |

1 | CFD design problems using progressive optimization - Dadone, Grossman - 1999 |