A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909305556434944 |
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| author | Kwok, Felix Tognon, Djahou N |
| author_facet | Kwok, Felix Tognon, Djahou N |
| contents | We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems. The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel. We then propose a preconditioner to speed up the convergence of GMRES in the special cases of the heat and wave equations. Numerical experiments are provided to illustrate the efficiency of our preconditioners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems Kwok, Felix Tognon, Djahou N Distributed, Parallel, and Cluster Computing Numerical Analysis We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems. The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel. We then propose a preconditioner to speed up the convergence of GMRES in the special cases of the heat and wave equations. Numerical experiments are provided to illustrate the efficiency of our preconditioners. |
| title | A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems |
| topic | Distributed, Parallel, and Cluster Computing Numerical Analysis |
| url | https://arxiv.org/abs/2406.11478 |