A recovered gradient method applied to smooth optimal shape problems
type: Item
instance of: scholarly article
title: A recovered gradient method applied to smooth optimal shape problems
zbMATH Open document ID: 0870.65050
author: I. Hlaváček
author: Jan Chleboun
published in: Applications of Mathematics
publication date: 1997-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/32951
review text: The article is devoted to sensitivity analysis in the optimal shape design. Several state problems based on elliptic boundary value problems are considered. The problems are formulated on a ``generalized rectangle'' whose upper side is formed by a design function which is a Bézier curve. The paper presents a new postprocessing technique suitable for quasiuniform triangulations which can be employed in the sensitivity analysis of optimal shape design problems. In the first part of the paper, a class of admissible domains is introduced, and the state problems and cost functionals are defined. Then, sensitivity formulae expressed by boundary integrals are derived for three standard cost functionals. There is also a section where the discretization by linear finite elements is discussed and the approximate optimization problems are defined. Finally, the authors recall the technique of recovered gradients on chevron triangulations and propose its application to the sensitivity formulae evaluation.
reviewed by: Petr Přikryl
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 90C52
zbMATH DE Number: 1046550
zbMATH Keywords: shape optimization
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: superconvergence
zbMATH Keywords: recovered gradient
MaRDI profile type: Publication
cites work: Q4732025
cites work: Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approches
cites work: A practical guide to splines
cites work: Q4281786
cites work: Q4839304
cites work: Q4040359
cites work: Design sensitivity analysis of structural systems
cites work: Optimization of the domain in elliptic problems by the dual finite element method
cites work: On the numerical solution of axisymmetric domain optimization problems
cites work: How to recover the gradient of linear elements on nonuniform triangulations
cites work: Q5689204
cites work: Shape optimization by means of the penalty method with extrapolation
cites work: Boundary flux estimates for elliptic problems by the perturbed variational method
cites work: On superconvergence techniques
cites work: Superconvergence analysis of approximate boundary-flux calculations
cites work: Q3972459
cites work: Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations
cites work: Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations
cites work: Q3948198
OpenAlex ID: W37198093
DOI: 10.21136/AM.1996.134327
Recommended article: Q4880633
Recommended article: Combining Sobolev smoothing with parameterized shape optimization
Recommended article: Discrete gradient flows for shape optimization and applications
Recommended article: An optimal gradient method for smooth strongly convex minimization
Recommended article: A Calculus for Non-smooth Shape Optimization with Applications to Geometric Inverse Problems
Recommended article: Shape optimization for Dirichlet problems: Relaxed solutions and optimality conditions
Recommended article: Optimization in the space of smooth shapes
Recommended article: A gradient-based, parameter-free approach to shape optimization
Recommended article: Approximation Methods for the Recovery of Shapes and Images from Gradients
Recommended article: Numerical gradients for shape optimization based on embedding domain techniques
description: scientific article; zbMATH DE number 1046550