Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives
type: Item
instance of: scholarly article
title: Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives
zbMATH Open document ID: 1453.65400
author: Shengfeng Zhu
published in: Journal of Optimization Theory and Applications
publication date: 2018-03-22T00:00:00Z
review text: The author considers a shape optimization issue for an eigenvalue Dirichlet boundary value problem attached to the Laplace equation. For this problem, a standard Ritz-Galerkin f. e. m. approximation along with its weak variational formulation are used during shape evolution. Then the author analyses two cases, a geometry constrained one and another unconstrained. Both are solved by two shape gradient descent algorithms based on shape sensitive analysis. Some interesting numerical experiments are carried out.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49R05
zbMATH DE Number: 6852045
zbMATH Keywords: shape optimization
zbMATH Keywords: eigenvalue
zbMATH Keywords: Eulerian derivative
zbMATH Keywords: shape functional
zbMATH Keywords: shape gradient
zbMATH Keywords: Galerkin finite element
reviewed by: Calin Ioan Gheorghiu
describes a project that uses: FreeFem++
MaRDI profile type: Publication
full work available at URL: s10957-017-1198-9
OpenAlex ID: W2769230031
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DOI: 10.1007/S10957-017-1198-9
description: scientific article; zbMATH DE number 6852045