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arXiv · 2412.02425

Efficient parallel inversion of ParaOpt preconditioners

Corentin Bonte·Arne Bouillon·Giovanni Samaey·Karl Meerbergen
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Abstract

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.

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Corentin Bonte, Arne Bouillon, Giovanni Samaey, Karl Meerbergen. 2024-12-03. Efficient parallel inversion of ParaOpt preconditioners. https://arxiv.org/abs/2412.02425

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