Non-overlapping Schwarz methods in time for parabolic optimal control problems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913476816928768 |
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| author | Gander, Martin Jakob Lu, Liu-Di |
| author_facet | Gander, Martin Jakob Lu, Liu-Di |
| contents | We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-overlapping Schwarz methods in time for parabolic optimal control problems Gander, Martin Jakob Lu, Liu-Di Numerical Analysis Optimization and Control We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers. |
| title | Non-overlapping Schwarz methods in time for parabolic optimal control problems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2408.12512 |