NDLI: Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Content Provider	Springer Nature Link
Author	Ballarin, Francesco Manzoni, Andrea Rozza, Gianluigi Salsa, Sandro
Copyright Year	2013
Abstract	Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.
Starting Page	537
Ending Page	563
Page Count	27
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	60
Issue Number	3
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2013-12-06
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shape optimization Computational fluid dynamics Free-form deformations Perturbation of identity Finite elements method Stokes equations Optimization of shapes other than minimal surfaces Optimal control problems involving partial differential equations Optimization and variational techniques Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Flow control and optimization Model reduction Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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