A topology-preserving level set method for shape optimization

Oleg Alexandrov; Fadil Santosa

doi:10.1016/j.jcp.2004.10.005

A topology-preserving level set method for shape optimization

Oleg Alexandrov
, Fadil Santosa

School of Mathematics

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.

Original language	English (US)
Pages (from-to)	121-130
Number of pages	10
Journal	Journal of Computational Physics
Volume	204
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2004.10.005
State	Published - Mar 20 2005

Bibliographical note

Funding Information:
We thank Grant Erdmann, whose suggestion that a logarithmic barrier method could be used to preserve constraints lead to the penalty functional we employ in this paper. We are grateful to the anonymous referees who made very helpful suggestions to the original manuscript, many of which we have incorporated in the present version. This work is supported in part by the National Science Foundation.

Keywords

Level set method
Optimization
Steepest descent method
Topology preservation

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10.1016/j.jcp.2004.10.005

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title = "A topology-preserving level set method for shape optimization",

abstract = "The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.",

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author = "Oleg Alexandrov and Fadil Santosa",

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AU - Santosa, Fadil

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N2 - The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.

AB - The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.

KW - Level set method

KW - Optimization

KW - Steepest descent method

KW - Topology preservation

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ER -

A topology-preserving level set method for shape optimization

Abstract

Bibliographical note

Keywords

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