Efficient parallel inversion of ParaOpt preconditioners
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916505804865536 |
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| author | Bonte, Corentin Bouillon, Arne Samaey, Giovanni Meerbergen, Karl |
| author_facet | Bonte, Corentin Bouillon, Arne Samaey, Giovanni Meerbergen, Karl |
| contents | Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient parallel inversion of ParaOpt preconditioners Bonte, Corentin Bouillon, Arne Samaey, Giovanni Meerbergen, Karl Numerical Analysis Optimization and Control Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems. |
| title | Efficient parallel inversion of ParaOpt preconditioners |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2412.02425 |