Hybrid Optimization Techniques for Multi-State Optimal Design Problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908839917387776 |
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| author | Erceg, Marko Kunštek, Petar Vrdoljak, Marko |
| author_facet | Erceg, Marko Kunštek, Petar Vrdoljak, Marko |
| contents | This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions. Existence of generalized solutions is established via a hybrid approach combining homogenization-based relaxation in the interior with suitable restrictions on admissible domains.
Based on this framework, we propose a numerical method that integrates homogenization and shape optimization. The domain boundary is evolved using a level set method driven by the shape derivative, while the interior material distribution is updated via an optimality criteria algorithm. The approach is demonstrated on a representative example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hybrid Optimization Techniques for Multi-State Optimal Design Problems Erceg, Marko Kunštek, Petar Vrdoljak, Marko Optimization and Control Analysis of PDEs 49Q10, 49K20, 65N30, 80M50 This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions. Existence of generalized solutions is established via a hybrid approach combining homogenization-based relaxation in the interior with suitable restrictions on admissible domains. Based on this framework, we propose a numerical method that integrates homogenization and shape optimization. The domain boundary is evolved using a level set method driven by the shape derivative, while the interior material distribution is updated via an optimality criteria algorithm. The approach is demonstrated on a representative example. |
| title | Hybrid Optimization Techniques for Multi-State Optimal Design Problems |
| topic | Optimization and Control Analysis of PDEs 49Q10, 49K20, 65N30, 80M50 |
| url | https://arxiv.org/abs/2602.16592 |