Optimal shape design for Stokes flow via minimax differentiability

Gao, Zhiming; Ma, Yichen; Zhuang, Hongwei

doi:10.1016/j.mcm.2007.10.006

Cited by 8 publications

(5 citation statements)

References 12 publications

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“…We refer to [27] for a general result on the differentiability of a min-max function, whereas in [28,32] some examples of shape differentiability of min-max functions are provided.…”

Section: Volumetric Shape Gradient Of the Compliance Via The Dual Mix...mentioning

confidence: 99%

Volumetric expressions of the shape gradient of the compliance in structural shape optimization

Giacomini,

Pantz,

Trabelsi

2017

Preprint

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In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear elasticity problem and we compute the volumetric expressions of the shape gradient of the compliance by means of the velocity method. A preliminary qualitative comparison of the two expressions of the shape gradient is performed through some numerical simulations using the Boundary Variation Algorithm.

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“…We refer to [27] for a general result on the differentiability of a min-max function, whereas in [28,32] some examples of shape differentiability of min-max functions are provided.…”

Section: Volumetric Shape Gradient Of the Compliance Via The Dual Mix...mentioning

confidence: 99%

Volumetric expressions of the shape gradient of the compliance in structural shape optimization

Giacomini,

Pantz,

Trabelsi

2017

Preprint

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“…The aim of this study is to investigate the energy minimization problem for the Oseen flow with velocity-pressure boundary conditions utilizing the so-called function space parametrization technique which was advocated by Delfour and Zolésio ([9])and was applied in [10,11]. The Oseen equations, which are the linearized Navier-Stokes equations, are the main component in an iterative scheme to solve the incompressible Navier-Stokes equations, for instance with a Picard iteration.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of a body in the Oseen flow

A-xia

Gao

2009

Numerical Methods Partial

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This article is concerned with a numerical simulation of shape optimization of the Oseen flow around a solid body. The shape gradient for shape optimization problem in a viscous incompressible flow is computed by the velocity method. The flow is governed by the Oseen equations with mixed boundary conditions containing the pressure. The structure of continuous shape gradient of the cost functional is derived by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. A gradient type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.

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“…In our article [8,10,11], we apply them to solve a Robin problem and shape reconstruction problems for the Stokes and Navier-Stokes flow, respectively.…”

Section: Introductionmentioning

confidence: 99%

Drag minimization for Navier–Stokes Flow

Gao¹,

Ma²,

Zhuang³

2008

Numerical Methods Partial

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This paper investigates the drag minimization in a two-dimensional flow which is governed by a nonhomogeneous Navier-Stokes equations. Two approaches are utilized to derive shape gradient of the cost functional. The first one is to use the shape derivative of the fluid state and its associated adjoint state; the second one is to utilize the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally, a gradient type algorithm is effectively formulated and implemented for the mentioned drag minimization problem.

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Optimal shape design for Stokes flow via minimax differentiability

Cited by 8 publications

References 12 publications

Volumetric expressions of the shape gradient of the compliance in structural shape optimization

Volumetric expressions of the shape gradient of the compliance in structural shape optimization

Shape optimization of a body in the Oseen flow

Drag minimization for Navier–Stokes Flow

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