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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17665 |
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| _version_ | 1866910312237629440 |
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| author | Hasebe, Takahiro Masamune, Jun Oka, Tomoyuki Sakai, Kota Yamada, Takayuki |
| author_facet | Hasebe, Takahiro Masamune, Jun Oka, Tomoyuki Sakai, Kota Yamada, Takayuki |
| contents | Motivated by recent progress of structural optimization problems, the paper presents a new method for constructing the distance function to the boundary of given sets of interest, which simplifies the optimization procedure. We extend the celebrated Varadhan's elliptic equation theory in 1967 by adding the source term to the equation, in which we encode the information about the set. We will also establish the rate of convergence in this new framework, which is sharp at least in the one-dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of signed distance functions with an elliptic equation Hasebe, Takahiro Masamune, Jun Oka, Tomoyuki Sakai, Kota Yamada, Takayuki Analysis of PDEs Primary: 35J57, Secondary: 74P20, 41A25 Motivated by recent progress of structural optimization problems, the paper presents a new method for constructing the distance function to the boundary of given sets of interest, which simplifies the optimization procedure. We extend the celebrated Varadhan's elliptic equation theory in 1967 by adding the source term to the equation, in which we encode the information about the set. We will also establish the rate of convergence in this new framework, which is sharp at least in the one-dimensional case. |
| title | Construction of signed distance functions with an elliptic equation |
| topic | Analysis of PDEs Primary: 35J57, Secondary: 74P20, 41A25 |
| url | https://arxiv.org/abs/2401.17665 |