A topology-preserving level set method for shape optimization

Authors:
Oleg Alexandrov;Fadil Santosa
Affiliations:
University of Minnesota School of Mathematics, Vincent Hall, 206 Church Str SE, Minneapolis MN 55455, USA;University of Minnesota School of Mathematics, Vincent Hall, 206 Church Str SE, Minneapolis MN 55455, USA
Venue:
Journal of Computational Physics
Year:
2005

Citing 7
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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.