A topology-preserving level set method for shape optimization

Oleg Alexandrov, Fadil Santosa

Research output: Contribution to journalArticlepeer-review

40 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 languageEnglish (US)
Pages (from-to)121-130
Number of pages10
JournalJournal of Computational Physics
Volume204
Issue number1
DOIs
StatePublished - 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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