A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems - Université de Paris - Faculté des Sciences
Conference Papers Year : 2024

A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems

Felix Kwok
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Abstract

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.
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Dates and versions

hal-04612018 , version 1 (14-06-2024)
hal-04612018 , version 2 (03-09-2024)
hal-04612018 , version 3 (05-09-2024)

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  • HAL Id : hal-04612018 , version 3

Cite

Felix Kwok, Djahou N Tognon. A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems. 63 rd IEEE Conference on Decision and Control, Dec 2024, Milan, Italy. ⟨hal-04612018v3⟩
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