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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.22724 |
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| _version_ | 1866909810303172608 |
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| author | Henríquez, Esteban Sánchez-Vizuet, Tonatiuh Solano, Manuel |
| author_facet | Henríquez, Esteban Sánchez-Vizuet, Tonatiuh Solano, Manuel |
| contents | We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising in the optimization process. The use of this strategy avoids the need for constant remeshing and enables a highly accurate description of the domain using a coarse computational mesh. We develop a rigorous analysis of the well-posedness of the problems that arise from the optimality conditions, and provide an a priori error analysis for the resulting discrete schemes. Numerical examples with manufactured problems are provided demonstrating the convergence of the scheme and the efficiency of the transfer path method. The approach proposed yields high resolution approximations of the boundary using grids with as few as 100 times less elements than an interpolatory technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An unfitted HDG discretization for a model problem in shape optimization Henríquez, Esteban Sánchez-Vizuet, Tonatiuh Solano, Manuel Numerical Analysis 49M41, 65N30 We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising in the optimization process. The use of this strategy avoids the need for constant remeshing and enables a highly accurate description of the domain using a coarse computational mesh. We develop a rigorous analysis of the well-posedness of the problems that arise from the optimality conditions, and provide an a priori error analysis for the resulting discrete schemes. Numerical examples with manufactured problems are provided demonstrating the convergence of the scheme and the efficiency of the transfer path method. The approach proposed yields high resolution approximations of the boundary using grids with as few as 100 times less elements than an interpolatory technique. |
| title | An unfitted HDG discretization for a model problem in shape optimization |
| topic | Numerical Analysis 49M41, 65N30 |
| url | https://arxiv.org/abs/2509.22724 |