A hierarchical approach for shape optimization

Beux, F.; Dervieux, Alain

doi:10.1108/02644409410799191

Cited by 36 publications

(51 citation statements)

References 6 publications

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“…This approach acts as a smoother and, on another hand, makes the convergence rate of the gradient-based method low dependent of the number of control parameters. The good behaviour observed in different numerical experiments (Beux, 1994;Beux et al, 1994), have been also corroborated by a theoretical view point in (Guillard, 1993;Guillard et al, 1995). Note that, contrary to the other approaches based on multigrid concepts, only one computational mesh is employed since the coarseness acts only on the number of design parameters.…”

Section: Introduction To Multi-level Approaches In Aerodynamic Shape supporting

confidence: 61%

“…The first test-case, already used for the multi-level approach associated to shape grid-point coordinates parametrisation (Beux, 1994;Beux et al, 1992;Beux et al, 1994;Held et al, 2002), is a 2D convergent-divergent nozzle inverse problem for inviscid subsonic flows (the flow is modelled, here, by the Euler equations). Here, the particular inverse problem is characterised by an initial constant-section nozzle and a target sine shape.…”

Section: Test-case 1: a 2d Nozzle Inverse Problemmentioning

confidence: 99%

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Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Martinelli

Beux

2008

European Journal of Computational Mechanics

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Section: Introduction To Multi-level Approaches In Aerodynamic Shape supporting

confidence: 61%

Section: Test-case 1: a 2d Nozzle Inverse Problemmentioning

confidence: 99%

Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Martinelli

Beux

2008

European Journal of Computational Mechanics

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“…This approach was first used in an aerodynamic optimisation setting by Beux and Dervieux 18 and has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19][20][21][22] , Bèzier surface FFD [23][24][25][26] , RBFs 27 and B-splines with a knot insertion algorithm 28,29 . In general, it was shown that implementation of multi-level nested parameterisations can improve the convergence rate, robustness and final solution of an optimisation procedure.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Masters

Taylor²,

Rendall

et al. 2017

AIAA Journal

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Subdivision curves are defined as the limit of a recursive application of a subdivision rule to an initial set of control points. This intrinsically provides a hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This work presents a shape parameterisation method based on this principle and investigates its application to aerodynamic optimisation. The subdivision curves are used to construct a multi-level aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then be periodically increased in resolution throughout. This brings the benefits of a low fidelity optimisation (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the multi-level subdivision parameterisation is tested on a variety of optimisation problems and compared to a control group of single-level subdivision schemes. For all the optimisation cases the multi-level schemes provided robust and reliable results in contrast to the single-level methods that often experienced difficulties with large numbers of design variables. As a result of this the multi-level methods exploited the high-dimensional design spaces better and consequently produced better overall results.

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“…This approach is akin to a multi-grid method for parameterisation and was first used in an aerodynamic optimisation setting by Beux and Dervieux [18]. It has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19,20,21,22], Bèzier surface FFD [23,24,25,26], RBFs [27] and B-Splines with a knot insertion algorithm [28,29].…”

Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Department of Aerospace Engineering, University of BristolThis work presents a shape parameterisation method based on multi-resolutional subdivision curves and investigates its application to aerodynamic optimisation. Subdivision curves are defined as the limit curve of a recursive application of a subdivision rule, which provides an intrinsically hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This is used to construct a progressive aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then periodically increased in resolution through the optimisation. This brings the benefits of a low dimensional design space (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the progressive refinement technique is tested on a variety of optimisation problems. For each problem a range of 'static' (non-progressive) subdivision schemes (equivalent to cubic B-splines) are also used as a control group. For all the optimisation cases the progressive schemes perform comparably or better than the static methods, often providing a significant computational advantage, and in many cases allowing a solution to be found when the static method would otherwise finish prematurely in a local optimum.

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A hierarchical approach for shape optimization

Cited by 36 publications

References 6 publications

Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

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