A framework for the construction of level set methods for shape optimization and reconstruction
type: Item
instance of: scholarly article
title: A framework for the construction of level set methods for shape optimization and reconstruction
zbMATH Open document ID: 1081.35134
DOI: 10.4171/IFB/81
author: Martin Burger
published in: Interfaces and Free Boundaries
publication date: 2004-03-08T00:00:00Z
review text: Summary: The aim of this paper is to develop a functional-analytic framework for the construction of level set methods, when applied to shape optimization and shape reconstruction problems. As a main tool we use a notion of gradient flows for geometric configurations such as used in the modelling of geometric motions in materials science. The analogies to this field lead to a scale of level set evolutions, characterized by the norm used for the choice of the velocity. This scale of methods also includes the standard approach used in previous work on this subject as a special case. Moreover, we apply this framework to some (inverse) model problems for elliptic boundary value problems. In numerical experiments we demonstrate that an appropriate choice of norms (dependent on the problem) yields stable and fast methods.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 65J20
zbMATH DE Number: 2052703
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: materials science
zbMATH Keywords: crystal growth
zbMATH Keywords: gradient flows
zbMATH Keywords: shape reconstruction
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/81
OpenAlex ID: W2002428563
description: scientific article; zbMATH DE number 2052703