Effect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization

Dwight, Richard P.; Brézillon, Joël

doi:10.2514/6.2006-690

Cited by 46 publications

(42 citation statements)

References 14 publications

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“…In this case approximations are also introduced in the matrices oH/oU L and oH/oU R of Eq. (12). This approximation saves a lot of human work [3].…”

Section: Approximation In the Discrete Adjointmentioning

confidence: 97%

“…In practice, it means that approximations are introduced in the matrices oU L /oU and oU R /oU of Eq. (12). The simplification is appreciable since the limiter implemented here requires a construction phase which is quite involved compared to that of mono-dimensional limiters [4].…”

Section: Approximation In the Discrete Adjointmentioning

confidence: 99%

“…In turn, these approximations can have a detrimental effect on the gradient accuracy [6,2,29,18,27]. To judge whether some of these approximations are acceptable, their effects on the optimization behavior should be considered [12,9]. These effects will be investigated here in terms of optimization results rather than only in terms of gradient accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Adjoint-based aerodynamic shape optimization on unstructured meshes

Carpentieri

Koren

Tooren

2007

Journal of Computational Physics

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In this paper, the exact discrete adjoint of an unstructured finite-volume formulation of the Euler equations in two dimensions is derived and implemented. The adjoint equations are solved with the same implicit scheme as used for the flow equations. The scheme is modified to efficiently account for multiple functionals simultaneously. An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to algorithms for constrained optimization, is tested on airfoil design cases involving transonic as well as supersonic flows. The effect of some approximations in the discrete adjoint, which aim at reducing the complexity of the implementation, is shown in terms of optimization results rather than only in terms of gradient accuracy. The shape-optimization method appears to be very efficient and robust.

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“…In this case approximations are also introduced in the matrices oH/oU L and oH/oU R of Eq. (12). This approximation saves a lot of human work [3].…”

Section: Approximation In the Discrete Adjointmentioning

confidence: 97%

Section: Approximation In the Discrete Adjointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adjoint-based aerodynamic shape optimization on unstructured meshes

Carpentieri

Koren

Tooren

2007

Journal of Computational Physics

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“…In particular the simple (not frequency domain) linearized code requires no more than four times the memory requirements of the non-linear code, and a single residual evaluation is 20%-40% cheaper in terms of CPU time. 19 The frequency domain residual however requires two products of a vector with the Jacobian, and hence a single evaluation is approximately 20%-60% more expensive than a non-linear residual on the same case.…”

Section: Linearized Frequency Domain Methodsmentioning

confidence: 99%

Linear Frequency Domain and Harmonic Balance Predictions of Dynamic Derivatives

Ronch

McCracken

Badcock

et al. 2013

Journal of Aircraft

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“…20) Four sections are parameterized along the wing span, and the locations are depicted in Fig. 11 (A-D).…”

Section: Case 1: Onera M6 Optimizationmentioning

confidence: 99%

Efficient Aeroelastic Design Optimization Based on the Discrete Adjoint Method

Zuo

Chen

et al. 2014

Trans. Japan Soc. Aero. S Sci.

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An approach for the aerodynamic optimization design of elastic configurations is implemented and tested. Aeroelastic analysis was carried out by combining an Euler equations solver and finite-element structural solver. Two important techniques used in high-fidelity aerostructural design optimization are discussed: the grid deformation method and finite-element mesh (FEM) update. An improved grid deformation methodology based on transfinite interpolation (TFI) and the radial basis function (RBF) method is presented. It adapts to complex configurations very well. The technique to update the FEM is based on a bilinear interpolation method and RBF method, and it adapts to any grid of finite-element model. The discrete adjoint method is used to get the gradient of the objective function with respect to design variables. Optimizations of a wing and a more realistic wing-body configuration are done to demonstrate the effectiveness of the proposed approach. Results show that the lift-to-drag ratio can be improved with constraints through optimization, which indicates that the present methodology can be successfully applied to design optimization of jig shapes of aircraft.

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Effect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization

Cited by 46 publications

References 14 publications

Adjoint-based aerodynamic shape optimization on unstructured meshes

Adjoint-based aerodynamic shape optimization on unstructured meshes

Linear Frequency Domain and Harmonic Balance Predictions of Dynamic Derivatives

Efficient Aeroelastic Design Optimization Based on the Discrete Adjoint Method

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