Asymptotic compatibility of parametrized optimal design problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916509932060672 |
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| author | Mengesha, Tadele Salgado, Abner J. Siktar, Joshua M. |
| author_facet | Mengesha, Tadele Salgado, Abner J. Siktar, Joshua M. |
| contents | We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this (modeling) parameter. We develop a framework that guarantees asymptotic compatibility, that is unconditional convergence with respect to modeling and discretization parameters to the solution of the corresponding limiting problems. This framework is then applied to two distinct classes of problems where the modeling parameter represents the degree of nonlocality. Specifically, we show unconditional convergence of optimal design problems when the state equation is either a scalar-valued fractional equation, or a strongly coupled system of nonlocal equations derived from the bond-based model of peridynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic compatibility of parametrized optimal design problems Mengesha, Tadele Salgado, Abner J. Siktar, Joshua M. Optimization and Control Numerical Analysis Analysis of PDEs 49M41, 49M25, 45F15, 65R20, 74P05 We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this (modeling) parameter. We develop a framework that guarantees asymptotic compatibility, that is unconditional convergence with respect to modeling and discretization parameters to the solution of the corresponding limiting problems. This framework is then applied to two distinct classes of problems where the modeling parameter represents the degree of nonlocality. Specifically, we show unconditional convergence of optimal design problems when the state equation is either a scalar-valued fractional equation, or a strongly coupled system of nonlocal equations derived from the bond-based model of peridynamics. |
| title | Asymptotic compatibility of parametrized optimal design problems |
| topic | Optimization and Control Numerical Analysis Analysis of PDEs 49M41, 49M25, 45F15, 65R20, 74P05 |
| url | https://arxiv.org/abs/2412.04630 |