A Topology-Preserving Level Set Method for Shape Optimization
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2004
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| _version_ | 1866908600103862272 |
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| author | Alexandrov, Oleg Santosa, Fadil |
| author_facet | Alexandrov, Oleg Santosa, Fadil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0405142 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | A Topology-Preserving Level Set Method for Shape Optimization Alexandrov, Oleg Santosa, Fadil Optimization and Control Numerical Analysis 49Q10 (primary); 49L99; 74P15 (secondary) 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. |
| title | A Topology-Preserving Level Set Method for Shape Optimization |
| topic | Optimization and Control Numerical Analysis 49Q10 (primary); 49L99; 74P15 (secondary) |
| url | https://arxiv.org/abs/math/0405142 |